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Popular >

simplify sqrt(4\sqrt{2)}

Solution

simplify

42

Solution

+1

Decimal Notation

2.37841 \dots

Solution steps

42

Apply radical rule:

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

42 = 42

= 42

4 = 2

= 22

Apply radical rule:

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

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

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

Apply radical rule:

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

2^{\frac{1}{2}} = (2^{\frac{1}{2}})^{\frac{1}{2}}

= 2 (2^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(2^{\frac{1}{2}})^{\frac{1}{2}} = 2^{\frac{1}{2} \cdot \frac{1}{2}}

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

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

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

Apply exponent rule:

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Frequently Asked Questions (FAQ)

What is sqrt(4\sqrt{2)} ?
The solution to sqrt(4\sqrt{2)} is 2\sqrt[4]{2}