Simplifying higher roots Quiz 1

Question 1

If the value of $$\sqrt{21-8\sqrt{5}}$$ is of the form $$a+b\sqrt{c}$$. Find the value of $$\sqrt[5]{ab+c}$$

Accepted Answer

1

Answer

-1

Answer

0

Answer

2

Question 2

If the value of $$4\sqrt{8}+3\sqrt{50}-6\sqrt{32}$$ is $$\alpha $$. Then find the roots of $${{x}^{2}}-5x+3{{\alpha }^{2}}=0$$.

Accepted Answer

2, 3

Answer

3, 5

Answer

3, 4

Answer

2, 5

Question 3

If the value of $$\sqrt[3]{\dfrac{2{{a}^{9}}{{b}^{4}}{{c}^{4}}}{54{{a}^{-6}}{{b}^{7}}{{c}^{-8}}}}$$ is $$\dfrac{{{a}^{p}}{{b}^{q}}{{c}^{r}}}{s}$$. Then find the value of  $$\dfrac{p+q+r}{s}$$

Accepted Answer

$$\dfrac{8}{3}$$

Answer

$$\dfrac{10}{3}$$

Answer

3

Answer

$$\dfrac{2}{3}$$

Question 4

If the value of $$\sqrt[3]{\dfrac{7\sqrt{27}+3\sqrt{12}-8\sqrt{48}}{4\left( 1+\sqrt{3} \right)\left( 3-\sqrt{3} \right)}}$$ is the common ratio of a G.P which has its first term as $$1$$. Find the sum of infinite terms of G.P

Accepted Answer

$$\dfrac{2}{2-\sqrt[3]{5}}$$

Answer

4

Answer

$$\dfrac{7}{8}$$

Answer

8

Question 5

If the value of $$\sqrt{\dfrac{\sqrt{4{{x}^{6}}}	imes \sqrt{64{{x}^{2}}}}{\sqrt[3]{{{x}^{12}}}}}$$is $$4\beta $$ and if $$\sqrt[7]{\beta }=\dfrac{2}{\cos \left( {{70}^{\circ }} ight)+1}-{{	an }^{2}}\left( 	heta  ight)$$. Then find the possible value of $$	heta $$

Accepted Answer

$${{35}^{\circ }}$$

Answer

$${{170}^{\circ }}$$

Answer

$${{70}^{\circ }}$$

Answer

$${{140}^{\circ }}$$