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Popular >

simplify 5sqrt(200)

Solution

simplify

5200

Solution

502

+1

Decimal Notation

70.71067 \dots

Solution steps

5200

Prime factorization of

200 : 2^{3} \cdot 5^{2}

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

Apply exponent rule:

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

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

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

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

= 5 2^{2} 2 5^{2}

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= 5 \cdot 22 5^{2}

Apply radical rule:

a^{2} = a, a \geq 0

5^{2} = 5

= 5 \cdot 22 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 5 \cdot 102

Multiply the numbers:

5 \cdot 10 = 50

= 502

Popular Examples

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simplify (x^2-y^2)/(x-y)simplify

\frac{x ^{2} - y ^{2}}{x - y}

((7^{16}+7^{14}))/(50)

\frac{( 7 ^{16} + 7 ^{14} )}{50}

Frequently Asked Questions (FAQ)

What is 5sqrt(200) ?
The solution to 5sqrt(200) is 50sqrt(2)