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Popular >

simplify sqrt(6*\sqrt{12)}

Solution

simplify

6 \cdot 12

Solution

+1

Decimal Notation

4.55901 \dots

Solution steps

612

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

612 = 612

= 612

Factor integer

6 = 2 \cdot 3

Apply radical rule:

2 \cdot 3 = 23

Factor integer

12 = 2^{2} \cdot 3

Apply radical rule:

Apply exponent rule:

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

Refine

Apply radical rule:

a a = a

22 = 2

Apply exponent rule:

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

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

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

= 2 \cdot 3^{\frac{3}{4}}

= 3^{\frac{3}{4}} \cdot 2

Popular Examples

\frac{3}{10} \div \frac{2}{7}

simplify 6*1/9 simplify

6 \cdot \frac{1}{9}

simplify 11/16*3/4 simplify

\frac{11}{16} \cdot \frac{3}{4}

simplify sqrt(36+4)simplify

36 + 4

simplify 2/3 x+3 simplify

\frac{2}{3} x + 3

Frequently Asked Questions (FAQ)

What is sqrt(6*\sqrt{12)} ?
The solution to sqrt(6*\sqrt{12)} is 2\sqrt[4]{3^3}