Question

√52x^4 solve ……………….

Answer 1

`\large\text{$2√(13)\;x^2$}`

Explanation:

Given expression:

`√(52x^4)`

Prime factorization is the process of representing a positive integer as a product of its prime factors.

The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:

`√(2^2 \cdot 13 \cdot x^4)`

`\textsf{Apply the radical rule:} \quad √(abc)=\sqrt{\vphantom{b}a}√(b)√(c)`

`√(2^2) √(13) √(x^4)`

`\textsf{Apply the radical rule:} \quad √(a^2)=a, \quad a \geq 0`

`2√(13) √(x^4)`

`\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{(m)/(n)},\quad \textsf{assuming} \;a\geq 0`

`2√(13) \;x^{(4)/(2)}`

`2√(13) \;x^2`

Therefore, the simplified expression is:

`\large\boxed{2√(13)\;x^2}`

Answer 2

2
`\sqrt{13x^(2) }`

Explanation:

To simplify the expression √52x^4, we can break it down as follows:

√(52x^4) = √(4 * 13 * x^4)

Since the square root of a product is equal to the product of the square roots, we can simplify further:

√(4 * 13 * x^4) = √4 * √13 * √(x^4)

The square root of 4 is 2, and the square root of x^4 is x^2:

2 * √13 * x^2

Therefore, the simplified expression is 2√13x^2.