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Popular >

simplify sqrt(216^')

Solution

simplify

21 6^{^{'}}

Solution

(66)^{'}

Solution steps

21 6^{^{'}}

Apply radical rule:

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

= (21 6^{^{^{'}}})^{\frac{1}{2}}

Apply exponent rule:

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

= 21 6^{^{^{'}} \frac{1}{2}}

Simplify

^{'} \frac{1}{2} : \frac{^{'}}{2}

= 21 6^{\frac{^{'}}{2}}

Prime factorization of

216 : 2^{3} \cdot 3^{3}

= (2^{3} \cdot 3^{3})^{\frac{^{'}}{2}}

Apply radical rule:

= (2^{3} \cdot 3^{3})^{^{^{'}}}

Apply exponent rule:

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

= (2 \cdot 3 \cdot 2^{2} \cdot 3^{2})^{^{^{'}}}

Apply radical rule:

= (2^{2} 3^{2} 2 \cdot 3)^{^{^{'}}}

Apply radical rule:

2^{2} = 2

= (2 3^{2} 2 \cdot 3)^{^{^{'}}}

Apply radical rule:

3^{2} = 3

= (2 \cdot 3 2 \cdot 3)^{^{^{'}}}

Refine

= (66)^{^{^{'}}}

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Frequently Asked Questions (FAQ)

What is sqrt(216^') ?
The solution to sqrt(216^') is (6sqrt(6))^'