What is sqrt(5)sqrt(5)sqrt(5) ?

The solution to sqrt(5)sqrt(5)sqrt(5) is 5sqrt(5)

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simplify sqrt(5)sqrt(5)sqrt(5)

simplify

555

55

Decimal Notation

11.18033 \dots

Solution steps

555

Apply exponent rule:

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

555 = 5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}} = 5^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

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

Combine the fractions

\frac{1}{2} + \frac{1}{2} + \frac{1}{2} : \frac{3}{2}

= 5^{\frac{3}{2}}

5^{\frac{3}{2}} = 5^{1 + \frac{1}{2}}

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

Apply exponent rule:

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

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

Refine

= 55

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What is sqrt(5)sqrt(5)sqrt(5) ?
The solution to sqrt(5)sqrt(5)sqrt(5) is 5sqrt(5)