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Popular >

simplify sqrt(16200)

Solution

simplify

16200

Solution

902

+1

Decimal Notation

127.27922 \dots

Solution steps

16200

Prime factorization of

16200 : 2^{3} \cdot 3^{4} \cdot 5^{2}

= 2^{3} \cdot 3^{4} \cdot 5^{2}

Apply exponent rule:

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

2^{3} \cdot 3^{4} \cdot 5^{2} = 2^{2} \cdot 2 \cdot 3^{4} \cdot 5^{2}

= 2^{2} \cdot 2 \cdot 3^{4} \cdot 5^{2}

2^{2} \cdot 2 \cdot 3^{4} \cdot 5^{2} = 2^{2} 2 3^{4} 5^{2}

= 2^{2} 2 3^{4} 5^{2}

Apply radical rule:

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

2^{2} = 2

= 22 3^{4} 5^{2}

3^{4} = 9

= 22 \cdot 9 5^{2}

Apply radical rule:

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

5^{2} = 5

= 22 \cdot 9 \cdot 5

Multiply the numbers:

2 \cdot 9 \cdot 5 = 90

= 902

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Frequently Asked Questions (FAQ)

What is sqrt(16200) ?
The solution to sqrt(16200) is 90sqrt(2)