Question

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

Answer 1

Answer: D. 100x32

Explanation:

Answer 2

Option (d) is correct.

`\sqrt{10000x^(64)}=100x^(32)`

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`

`=√(10000)\sqrt{x^(64)}`

Factor 10000 as
`10000=100^2`

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

`√(100^2)=100`

also,
`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{(m)/(n)},\:\quad \mathrm{\:assuming\:}a\ge 0`

We have,

`\sqrt{x^(64)}=x^{(64)/(2)}=x^(32)`

Thus,
`\sqrt{10000x^(64)}=100x^(32)`