Simplification-Test 4 (Based on Fractions/Square roots and Cube roots)

Answer: Option D

Explanation

Here, 

$$\begin{gathered} =784\times \sqrt{\left(256\right)}\times 343=4^4\times 7^x \\ =784\times 16\times 343=4^4\times 7^x \\ =(28{)}^2\times 16\times 7^3=4^4\times 7^x \\ =7^5\times 4^4=4^4\times 7^x \\ =x=5 \end{gathered}$$

Hence, Option D is correct.

Answer: Option D

Explanation

Here,

$$\begin{gathered} = \sqrt{\left(5\right)\times \sqrt{\left(1600\right)\times \sqrt{\left(1024\right)}}}=28÷7\times x \\ =\sqrt{5\times \sqrt{16000\times 1024}}=4x \\ =\sqrt{5\times 1280}=4x \\ =8\times 10=4x \\ =x=20 \end{gathered}$$

Hence, Option D is correct.

Answer: Option A

Explanation

Here,

⇒ √625×12-864÷24= x+71

⇒ 25×12-36=x+71

⇒ 300-36=x+71

∴ x=193

Hence, option A is correct

Answer: Option A

Explanation

Here,

$$\begin{gathered} =\frac{{\left(216\right)}^{{\displaystyle \frac{1}{3}}}\times {26}^4\times {\left(39\right)}^4}{{\left(12\right)}^4\times 3\times 2^{-3}}={13}^x \\ =\frac{6\times 2^4\times 3^4\times {13}^8}{{\left(2\times 6\right)}^4\times 3\times 2^{-2}}={13}^x \\ =\frac{6\times 6^4\times {13}^8}{6\times 6^4}={13}^x \\ ={13}^8=13 \\ =x=8 \end{gathered}$$

Hence, Option A is correct.

Answer: Option C

Explanation

Here,

We can do it directly by adding least number from the option.

So, 1020+4=1024 and 1024 is a perfect square.