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Popular >

simplify 4sqrt(200)

Solution

simplify

4200

Solution

402

+1

Decimal Notation

56.56854 \dots

Solution steps

4200

Prime factorization of

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

= 4 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}

= 4 2^{2} \cdot 2 \cdot 5^{2}

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

= 4 2^{2} 2 5^{2}

Apply radical rule:

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

2^{2} = 2

= 4 \cdot 22 5^{2}

Apply radical rule:

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

5^{2} = 5

= 4 \cdot 22 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 4 \cdot 102

Multiply the numbers:

4 \cdot 10 = 40

= 402

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Frequently Asked Questions (FAQ)

What is 4sqrt(200) ?
The solution to 4sqrt(200) is 40sqrt(2)