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Popular >

simplify 3sqrt(5/3 \sqrt{5)}

Solution

simplify

3 \frac{5}{3} 5

Solution

3 \cdot 5^{\frac{3}{4}}

+1

Decimal Notation

5.79146 \dots

Solution steps

3 \frac{5}{3} 5

\frac{5}{3} 5 = \frac{5 5}{3}

= 3 \frac{5 5}{3}

Apply exponent rule:

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

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

Multiply

3^{2} \cdot \frac{5 5}{3} : 155

= 155

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 155

Factor integer

15 = 5 \cdot 3

Apply radical rule:

5 \cdot 3 = 53

Apply exponent rule:

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

= 3 \cdot 5^{\frac{1}{2} + \frac{1}{4}}

5^{\frac{1}{2} + \frac{1}{4}} = 5^{\frac{3}{4}}

= 3 \cdot 5^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is 3sqrt(5/3 \sqrt{5)} ?
The solution to 3sqrt(5/3 \sqrt{5)} is sqrt(3)*5^{3/4}