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Popular >

simplify (sqrt(5))^{5/2}

Solution

simplify

(5)^{\frac{5}{2}}

Solution

5 \cdot 5^{\frac{1}{4}}

+1

Decimal Notation

7.47674 \dots

Solution steps

(5)^{\frac{5}{2}}

Apply exponent rule:

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

= 5^{\frac{1}{2} \cdot \frac{5}{2}}

\frac{1}{2} \cdot \frac{5}{2} = \frac{5}{4}

= 5^{\frac{5}{4}}

5^{\frac{5}{4}} = 5^{1 + \frac{1}{4}}

= 5^{1 + \frac{1}{4}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 5^{1} \cdot 5^{\frac{1}{4}}

Refine

= 5 \cdot 5^{\frac{1}{4}}

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Frequently Asked Questions (FAQ)

What is (sqrt(5))^{5/2} ?
The solution to (sqrt(5))^{5/2} is 5*5^{1/4}