Title: MAT. Arrels. Operacions
Course: Matemàtiques de 3r d'ESO

Feedback shared by this category's questions, if right: La teva resposta és correcta.
Feedback shared by this category's questions, if partly right: 1
Feedback shared by this category's questions, if wrong: La teva resposta és incorrecta.

Q: Resoleu: $$x^3-{{={a}+{b}+{c}}}x^2+{{={a}*{b}+{a}*{c}+{b}*{c}}}x-{{={a}*{b}*{c}}}=0$$
- {a}
- {b}
- {c}
- {={c}+1}
- {={a}-1}
- {={a}-2}
- {={b}-1}
- {={b}-2}
- {={c}+2}
- {={c}-2}
- {={c}-1}
A: {a} (formula; values not in the backup's text) / {b} (formula; values not in the backup's text) / {c} (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $$\frac{\frac{{a}+\sqrt{{={c}*{d}*{d}}}}{\sqrt{{={p}*{p}*{p}}}+\sqrt{{p}}}}{\frac{\sqrt{{p}}}{\sqrt{{c}}+{b}}}$$
- $$\frac{{a}\sqrt{{c}}+{b}\sqrt{{={c}*{d}*{d}}}}{\sqrt{{={p}*{p}*{p}*{p}}}+\sqrt{{={p}*{p}}}}$$
- $$\frac{{={a}*{b}+{c}*{d}}+{={a}+{b}*{d}}\sqrt{{c}}}{{={p}*{p}+{p}}}$$
- $$\frac{\sqrt{{=({a}+{c}*{d}*{d})*({c}+{b})}}}{\sqrt{{={p}*{p}*{p}*{p}+{p}*{p}}}}$$
- $$\frac{{={a}+{b}}\sqrt{{={c}*{d}*{d}}}}{{{={p}*{p}+1}}\sqrt{{p}}}$$
- $$\frac{{=17*{a}-13*{b}}\sqrt{{c}}}{{{=2*{p}+1}}\sqrt{{p}}}$$
- $$\frac{{={a}*{b}*13-3*{c}*{d}}+{=13*{a}-{b}*{d}}\sqrt{{c}}}{{=3*{p}}}$$
- $$\frac{{={a}+{b}+{c}*{d}}+{={a}+{b}*{d}-4}\sqrt{{={c}*{d}*{d}}}}{{={p}}}$$
- $$\frac{{=17*{a}-{c}*{d}}+{={a}+{b}+{d}}\sqrt{{p}}}{{={c}}}$$
A: $$\frac{{={a}*{b}+{c}*{d}}+{={a}+{b}*{d}}\sqrt{{c}}}{{={p}*{p}+{p}}}$$ (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $$\frac{\sqrt{{p}}}{{b}}\cdot\frac{\sqrt{{={p}*{q}}}}{{a}}+\frac{\sqrt{{r}}}{{a}}\cdot\frac{\sqrt{{={r}*{q}}}}{{c}}$$
- 1
- $$\frac{\sqrt{{={p}*{q}*{p}+{r}*{q}*{r}}}}{{={a}*{b}+{a}*{c}}}$$
- $$\frac{\sqrt{{={p}*{q}*{p}}}+\sqrt{{={r}*{q}*{r}}}}{{={a}*{b}+{a}*{c}}}$$
- $$\frac{{={a}*{c}}\sqrt{{={p}*{q}}}+{={a}*{b}}\sqrt{{={r}*{q}}}}{{={a}*{a}*{b}*{c}}}$$
- $$\frac{{={c}*{p}+{b}*{r}}\sqrt{{q}}}{{={a}*{b}*{c}}}$$
- $$\frac{{{c}}\sqrt{{={p}*{q}*{p}}}+{{b}}\sqrt{{={r}*{q}*{r}}}}{{={a}*{a}*{b}*{c}}}$$
- $$\frac{{={a}*{c}}\sqrt{{={p}*{q}}}+{={a}*{b}}\sqrt{{={r}*{q}}}}{{={a}*{b}*{c}}}$$
A: $$\frac{{={c}*{p}+{b}*{r}}\sqrt{{q}}}{{={a}*{b}*{c}}}$$ (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $$\frac{\sqrt{{a}}}{{={p}*{r}}}+\frac{\sqrt{{c}}}{{={p}*{q}}}$$
- $$\frac{{={q}*{p}}\sqrt{{a}}+{={r}*{p}}\sqrt{{c}}}{{={r}*{q}}}$$
- $$\frac{{q}\sqrt{{a}}+{r}\sqrt{{c}}}{{={p}*{r}*{q}}}$$
- $$\frac{\sqrt{{a}}+\sqrt{{c}}}{{={p}*{r}+{p}*{q}}}$$
- $$\frac{\sqrt{{={a}+{c}}}}{{={p}*{r}+{p}*{q}}}$$
- $$\frac{\sqrt{{={a}*{c}}}}{{={p}*{r}+{p}*{q}}}$$
- $$\frac{\sqrt{{={a}*{c}}}}{{={p}*{r}*{p}*{q}}}$$
- $$\frac{{q}\sqrt{{a}}+{r}\sqrt{{c}}}{{={p}*{r}*{p}*{q}}}$$
- $$\frac{\sqrt{{={a}+{c}}}}{{={p}*{r}*{p}*{q}}}$$
A: $$\frac{{q}\sqrt{{a}}+{r}\sqrt{{c}}}{{={p}*{r}*{q}}}$$ (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $$\frac{\sqrt{{a}}}{{d}}(\frac{\sqrt{{b}}}{{e}}-\frac{\sqrt{{b}}}{{f}})$$
- $$0$$
- $$\frac{\sqrt{{={a}*{b}}}}{{={d}*({e}-{f})}}$$
- $$\frac{{={f}-{e}}\sqrt{{={a}*{b}}}}{{={d}*{e}*{f}}}$$
- $$\frac{{={e}*{f}}\sqrt{{a}}}{{={d}*({f}-{e})}\sqrt{{b}}}$$
- $$\frac{{={e}-{f}}\sqrt{{={a}*{b}}}}{{={d}*{e}*{f}}}$$
- $$\frac{\sqrt{{={a}*{b}}}}{{={d}*{e}*{f}}}$$
A: $$\frac{{={f}-{e}}\sqrt{{={a}*{b}}}}{{={d}*{e}*{f}}}$$ (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $${c} \sqrt{{={a}*{a}*{b}*{b}*{b}}} - {d} \sqrt{{={a}*{a}*{a}*{a}*{b}}}$$
- No es pot simplificar
- Una altra esposta
- $${={c}-{d}} \sqrt{{={a}*{a}*{b}*{b}*{b}-{a}*{a}*{a}*{a}*{b}}}$$
- $${={c}*{a}*{b}-{d}*{a}*{a}}\sqrt{{b}}$$
- $${={c}*{a}*{b}-{d}*{a}*{a}}$$
- $${={a}*({c}-{d})} \sqrt{{={b}*({b}*{b}-{a}*{a})}}$$
- $${={a}*{c}-{d}*{a}*{a}} \sqrt{{={b}*{b}*{b}-{b}}}$$
- $${={b}*{c}-{d}*{a}} \sqrt{{={a}}}$$
- $${={b}*{c}-{d}*{a}} \sqrt{{={b}*{a}}}$$
- $${={b}*{c}-{d}*{a}} \sqrt{{={a}*{b}-{c}}}$$
A: $${={c}*{a}*{b}-{d}*{a}*{a}}\sqrt{{b}}$$ (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $$\sqrt{{={a}*{a}*{b}}}+\sqrt{{={c}*{c}*{b}}}$$
- $$\sqrt{{={a}*{a}*{b}+{c}*{c}*{b}}}$$
- $${={a}*{a}+{c}*{c}}\sqrt{{b}}$$
- $$\sqrt[4]{{={a}*{a}*{b}+{c}*{c}*{b}}}$$
- $${{={a}*{b}+{c}*{b}}}$$
- $${={a}+{c}}\sqrt{{b}}$$
- No es pot simplificar
- Un altre resultat
- $${=2*({a}+{c})}\sqrt{{b}}$$
- $${{={a}*{b}*{c}}}$$
- $${={a}+{c}}\sqrt{{=2*{b}}}$$
A: $${={a}+{c}}\sqrt{{b}}$$ (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $${c} \sqrt{{={a}*{b}*{b}}} \cdot {d} \sqrt{{={a}}}$$
- $${={c}*{d}} \sqrt{{={a}*{b}*{b}}}$$
- $${={c}*{d}*{b}} \sqrt{a}$$
- No es pot simplificar
- Un altre resultat
- $${={c}*{d}*{b}*{a}}$$
- $${={c}*{d}} \sqrt[4]{{={a}*{a}*{b}*{b}}}$$
- $${={c}*{d}} \sqrt{{={a}*{b}}}$$
- $$ \sqrt{{={a}*{b}*{a}*{b}*{c}*{d}}}$$
- $$ \sqrt[4]{{={a}*{b}*{a}*{b}*{c}*{d}}}$$
A: $${={c}*{d}*{b}*{a}}$$ (formula; values not in the backup's text)

Q: $$\frac{\sqrt[3]{2}}{\sqrt[5]{2}}$$
- $$2^{-2}$$
- $$\frac{1}{\sqrt{2}}$$
- $$\sqrt[15]{1}$$
- $$\sqrt[15]{4}$$
A: $$\sqrt[15]{4}$$

Q: $$\sqrt{2}\sqrt{7}$$
- $$\sqrt{14}$$
- $$\sqrt[4]{14}$$
- No es pot fer
A: $$\sqrt{14}$$

Q: Marca les igualtats correctes
- $$\sqrt{15}\cdot \sqrt{3}=\sqrt{45}$$
- $$\frac{\sqrt{15}}{\sqrt{3}}=\sqrt{5}$$
- $$\sqrt{15}+ \sqrt{3}=\sqrt{18}$$
- $$\(\sqrt{15}\)^3=\sqrt{125}$$
- $$\sqrt[3]{\sqrt[4]{10}}=\sqrt[7]{10}$$
- $$\sqrt[3]{\sqrt[4]{10}}=\sqrt[12]{10}$$
A: $$\sqrt{15}\cdot \sqrt{3}=\sqrt{45}$$; $$\frac{\sqrt{15}}{\sqrt{3}}=\sqrt{5}$$; $$\sqrt[3]{\sqrt[4]{10}}=\sqrt[12]{10}$$

Q: Calcula $$\sqrt[7]{\sqrt[3]{a}}$$
- $$\sqrt[4]{a}$$
- $$\sqrt[10]{a}$$
- $$\sqrt[21]{a}$$
- $$a^{\frac{3}{7}}$$
A: $$\sqrt[21]{a}$$

Q: Calcula $$(\sqrt{7}+\sqrt{5})^2$$
- $$5\sqrt{7}+7\sqrt{5}$$
- $$\sqrt{144}$$
- $$2+2\sqrt{35}$$
- $$12$$
- $$12+2\sqrt{35}$$
A: $$12+2\sqrt{35}$$

Q: Racionalitza $$\frac{5}{3-\sqrt{2}}$$
- $$\frac{5(3+\sqrt{2})}{11}$$
- $$\frac{5(3+\sqrt{2})}{7}$$
- $$\frac{3-\sqrt{2}}{5}$$
- $$\frac{5(3-\sqrt{2})}{7}$$
- $$\frac{5(3-\sqrt{2})}{11}$$
- $$\frac{5}{3-\sqrt{2}}$$
A: $$\frac{5(3+\sqrt{2})}{7}$$

Q: És cert $$\sqrt[n]{a+b}=\sqrt[n]{a}+\sqrt[n]{b}$$ ?
- Vertader
- Fals
A: Fals

Q: Extreu tots els factors possibles: $$\sqrt{\frac{27a^2}{16b^3}}$$
- $$\frac{a}{4}\sqrt{\frac{27}{b^3}}$$
- $$\frac{3a}{4b}\sqrt{\frac{3}{b}}$$
- $$\frac{a^2}{b^2}\sqrt{\frac{27}{16b}}$$
- $$\frac{a^2}{4b^2}\sqrt{\frac{27}{b}}$$
- $$\frac{a^2}{b^3}\sqrt{\frac{27}{16}}$$
A: $$\frac{3a}{4b}\sqrt{\frac{3}{b}}$$

Q: Extreu factors de $$\sqrt{20}$$
- $$2\sqrt{5}$$
- $$5\sqrt{2}$$
- $$2\sqrt{10}$$
- $$10\sqrt{2}$$
A: $$2\sqrt{5}$$

Q: Extreu factors de $$\sqrt[3]{48}$$
- $$16\sqrt[3]{3}$$
- $$2\sqrt[3]{3}$$
- $$\sqrt[3]{16}$$
- $$2\sqrt[3]{6}$$
A: $$2\sqrt[3]{6}$$

Q: $$\sqrt{15}+\sqrt{60}+\sqrt{1500}$$
- Cap de les altres
- $$13\sqrt{15}$$
- $$\sqrt{1575}$$
- $$\sqrt{75}+\sqrt{1500}$$
A: $$13\sqrt{15}$$

Q: $$(\sqrt{6}+\sqrt{5})(\sqrt{6}-\sqrt{5})$$
- 11
- 1
- 9
- $$2\sqrt{30}$$
- $$\sqrt{61}$$
- 3
A: 1

Q: $$\frac{\frac{\sqrt{{a}}}{{b}}}{\frac{\sqrt{{={a}*{d}*{d}}}}{{c}}}$$

OP1: No es pot simplificar

OP2: Una altra solució

OP3: $$\frac{{c}}{{={b}*{d}}}$$

OP4: $$\frac{{={b}*{d}}}{{c}}$$

OP5: $$\frac{\sqrt{{={a}/{b}}}}{\sqrt{{={a}*{d}*{d}/{c}}}}$$

OP6: $$\frac{\sqrt{{={a}*{d}*{d}/{c}}}}{\sqrt{{={a}/{b}}}}$$

OP7: $$\frac{{d}}{{={b}*{c}}}$$

OP8: $$\frac{{={b}*{c}}}{{d}}$$

OP9: $$\frac{{={b}*{c}}}{{={a}*{d}}}$$

OP10: $$\frac{{={a}*{d}}}{{={b}*{c}}}$$

OP11: $$\frac{{={a}}}{{={b}*{c}}}$$

OP12: $$\frac{{={b}*{c}}}{{={a}}}$$

OP13: $$\frac{\sqrt{{={a}*{a}*{d}*{d}}}}{{={b}*{c}}}$$

OP14: $$\frac{{={b}*{c}}}{\sqrt{{={a}*{a}*{d}*{d}}}}$$

OP15: $$\frac{\sqrt{{d}}}{{={b}*{c}}}$$

OP16: $$\frac{{={b}*{c}}}{\sqrt{{d}}}$$

OP17: $$\frac{{={a}*{b}}}{{={a}*{d}*{d}*{c}}}$$

OP18: $$\frac{{={a}*{d}*{d}*{c}}}{{={a}*{b}}}$$

OP19: $$\frac{{={a}*{b}}}{{={c}*{d}}}$$

OP20: $$\frac{{={c}*{d}}}{{={a}*{b}}}$$
- OP{=1+{a}-{a}}
- OP{=2+{a}-{a}}
- OP{=3+{a}-{a}}
- OP{=4+{a}-{a}}
- OP{=5+{a}-{a}}
- OP{=6+{a}-{a}}
- OP{=7+{a}-{a}}
- OP{=8+{a}-{a}}
- OP{=9+{a}-{a}}
- OP{=10+{a}-{a}}
- OP{=11+{a}-{a}}
- OP{=12+{a}-{a}}
- OP{=13+{a}-{a}}
- OP{=14+{a}-{a}}
- OP{=15+{a}-{a}}
- OP{=16+{a}-{a}}
- OP{=17+{a}-{a}}
- OP{=18+{a}-{a}}
- OP{=19+{a}-{a}}
- OP{=20+{a}-{a}}
A: OP{=3+{a}-{a}} (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: $$(\sqrt{{b}}+\sqrt{{a}})(\sqrt{{={b}*{a}}}+\sqrt{{={b}*{a}*{a}*{a}}})$$

OP1: Una altra resposta

OP2: No es pot simplificar

OP3: $$\sqrt{{={b}+{a}+{b}*{a}+{b}*{a}*{a}*{a}}}$$

OP4: $${={b}+{a}*{b}} \sqrt{{a}}+{={a}+{a}*{a}} \sqrt{{b}}$$

OP5: $$\sqrt{{=({b}+{a})*({b}*{a}+{b}*{a}*{a}*{a})}}$$

OP6: $$\sqrt{{={a}*{b}*{b}}}+\sqrt{{={a}*{a}*{a}*{a}*{b}}}$$

OP7: $$\sqrt{{={a}*{b}*{b}+{a}*{a}*{a}*{a}*{b}}}$$

OP8: $${b} \sqrt{{a}}+{={a}*{a}} \sqrt{{b}}$$

OP9: $${={b}*{b}} \sqrt{{a}}+{={a}*{a}} \sqrt{{b}}$$

OP10: $${={b}+2} \sqrt{{a}}+{={a}*{a}-1} \sqrt{{b}}$$

OP11: $${={b}+1}\sqrt{{a}}+{={a}*{a}-1}\sqrt{{b}}$$
- OP{=1+{a}-{a}}
- OP{=2+{a}-{a}}
- OP{=3+{a}-{a}}
- OP{=4+{a}-{a}}
- OP{=5+{a}-{a}}
- OP{=6+{a}-{a}}
- OP{=7+{a}-{a}}
- OP{=8+{a}-{a}}
- OP{=9+{a}-{a}}
- OP{=10+{a}-{a}}
- OP{=11+{a}-{a}}
A: OP{=4+{a}-{a}} (formula; values not in the backup's text)
If partly right: La teva resposta és parcialment correcta.

Q: Quants nombres del conjunt {2, 3, 4, ..., {={n}-2}, {={n}-1}, {n}} són quadrats perfectes?
A: floor(sqrt({n}))-1 (formula; values not in the backup's text)

Q: Quants nombres del conjunt {2, 3, 4, ..., {={n}-2}, {={n}-1}, {n}} són cubs perfectes?
A: floor(pow({n},1/3))-1 (formula; values not in the backup's text)

Q: Calculeu SENSE calculadora $$\sqrt{{={n}*{n}}}$$
A: {n} (formula; values not in the backup's text)

Q: Calculeu SENSE calculadora $$\sqrt 1$$
A: 1

Q: Calculeu AMB calculadora $$\sqrt 2$$
A: 1.4142135623731 (± 0.0001)

Q: Calculeu AMB calculadora $$\sqrt{{={n}*({n}-{k})}}$$
A: sqrt({n}*({n}-{k})) (formula; values not in the backup's text)

Q: Trobeu un número que multiplicat per ell mateix doni {={n}*{n}}.
A: {n} (formula; values not in the backup's text)

Q: Trobeu un número que multiplicat per ell mateix doni {={n}*({n}-{k})}
A: sqrt({n}*({n}-{k})) (formula; values not in the backup's text)

Q: Una capsa de bombons té el mateix nombre de files que bombons caben a cada fila (per exemple: si a cada fila caben 4 bombons, tindrà 4 files). Penseu en diverses capses d'aquest tipus.

L'Anna ha intentat distribuir els seus {={n}*{n}+{r}} bombons en la capsa però li n'han sobrat uns pocs. Quantes files té la capsa? quants bombons li han sobrat?

Introduïu les respostes SEPARADES PER COMA: files,sobrants. Així si, per exemple, la solució és que la caixa té 5 files i sobren 2 bombons, caldria introduir 5,2. Sense unitats.
A: {n}+{r}/10 (formula; values not in the backup's text)