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Popular >

simplify \sqrt[4]{(343)^2}

Solution

simplify

Solution

77

+1

Decimal Notation

18.52025 \dots

Solution steps

Apply radical rule:

= ((343)^{2})^{\frac{1}{4}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (343)^{2 \cdot \frac{1}{4}}

2 \cdot \frac{1}{4} = \frac{1}{2}

= (343)^{\frac{1}{2}}

a^{\frac{1}{2}} = a

= 343

Prime factorization of

343 : 7^{3}

= 7^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= 7^{2} \cdot 7

Apply radical rule:

= 7 7^{2}

Apply radical rule:

7^{2} = 7

= 77

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{(343)^2} ?
The solution to \sqrt[4]{(343)^2} is 7sqrt(7)