Question

What is the simplified form of √10000x^64 ? 5000x^32 5000x^8 100x^8 100x^32

Answer 1

Answer:

Option (d) is correct.

$\sqrt{10000x^{64}}=100x^{32}$

Step-by-step explanation:

Given : Expression $\sqrt{10000x^{64}}$

We have to write a simplified form of the given expression $\sqrt{10000x^{64}}$

Consider the given expression $\sqrt{10000x^{64}}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0$

$=\sqrt{10000}\sqrt{x^{64}}$

Factor 10000 as $10000=100^2$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt{100^2}=100$

also, $\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0$

We have,

$\sqrt{x^{64}}=x^{\frac{64}{2}}=x^{32}$

Thus, $\sqrt{10000x^{64}}=100x^{32}$

Answer 2

Answer: D. 100x32

Step-by-step explanation: