Simplification-Test 5 (Based on Square roots and Cube roots/Surds and Indices)

Answer: Option E

Explanation

$\sqrt[3]{804357}={93}^{3 \mathrm{x}\frac{1}{3}}=93$

Hence Option E is correct.

Answer: Option D

Explanation

$\begin{array}{l}\text{Here,}\\ {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(12)}}^{\text{2}}{\text{+ (?)}}^{\text{2}}{\text{+ (7)}}^{\text{2}}\text{= 274}\\ \\ \Rightarrow {\text{ \hspace{0.17em}144 + (?)}}^{\text{2}}\text{+ 49 = 274}\\ \\ \Rightarrow {\text{ \hspace{0.17em}\hspace{0.17em}(?)}}^{\text{2}}\text{+ 193 = 274}\\ \\ \Rightarrow {\text{ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(?)}}^{\text{2}}\text{= 274}-\text{193}\\ \\ \Rightarrow {\text{ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(?)}}^{\text{2}}\text{= 81}\\ \\ \text{[on taking square root both sides]}\\ \\ \Rightarrow \text{ ?=}\sqrt{\text{81}}\text{=9}\end{array}$

Hence Option D is correct.

Answer: Option E

Explanation

$\begin{array}{l}\text{Here,}\\ \\ \Rightarrow {\text{(?)}}^{\text{2}}{\text{+ (65)}}^{\text{2}}{\text{= (160)}}^{\text{2}}-{\text{(90)}}^{\text{2}}-\text{7191}\\ \\ \Rightarrow {\text{ (?)}}^{\text{2}}{\text{= (160)}}^{\text{2}}-{\text{(90)}}^{\text{2}}-\text{7191}-{\text{(65)}}^{\text{2}}\\ \\ \Rightarrow {\text{ (?)}}^{\text{2}}\text{ = 25600}-\text{(8100 + 7191 + 4225)}\\ \\ \Rightarrow {\text{ (?)}}^{\text{2}}\text{ = 25600}-\text{19516}\\ \\ \Rightarrow {\text{ (?)}}^{\text{2}}\text{ = 6084 }\Rightarrow \text{\hspace{0.17em}\hspace{0.17em}(?) = }\sqrt{\text{6084}}\text{ = 78}\end{array}$

Hence, Option E is correct.

Answer: Option A

Explanation

$\begin{array}{l}\text{Here,\hspace{0.17em}}\\ \\ \Rightarrow \sqrt{{\text{(8)}}^{\text{2}}\times \text{7}\times {\text{(5)}}^{\text{2}}-\text{175}}\text{ =?}\\ \\ \Rightarrow \sqrt{64\times \text{7}\times 2\text{5}-\text{175}}=?\\ \\ \Rightarrow \sqrt{11200-\text{175}}=?\\ \\ \Rightarrow \sqrt{11025}=105\end{array}$

Hence, Option A is correct.

Answer: Option E

Explanation

In this above question 

We use factorisation method and solve

$\begin{array}{l}\Rightarrow \text{? = 1225 = 5}\times \text{5}\times \text{7}\times \text{7}\\ \\ \Rightarrow \text{ ? =}\sqrt{\text{1225}}\text{ = }\sqrt{\text{5}\times \text{5}\times \text{7}\times \text{7}}\\ \\ \Rightarrow \text{ ? = 5}\times \text{7 \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(}\because \text{in square root, to}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}remove root, we take pairs of two]}\\ \\ \Rightarrow ?\text{=5}\times \text{7=35}\end{array}$

Hence, Option E is correct.