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Popular >

simplify sqrt(100^3)

Solution

simplify

10 0^{3}

Solution

1000

Solution steps

10 0^{3}

Apply exponent rule:

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

10 0^{2 + 1} = 10 0^{2} \cdot 100

= 10 0^{2} \cdot 100

Apply radical rule:

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

10 0^{2} \cdot 100 = 10 0^{2} 100

= 10 0^{2} 100

Apply radical rule:

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

10 0^{2} = 100

= 100100

Prime factorization of

100 : 2^{2} \cdot 5^{2}

= 100 2^{2} \cdot 5^{2}

Apply radical rule:

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

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

= 100 2^{2} 5^{2}

Apply radical rule:

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

2^{2} = 2

= 100 \cdot 2 5^{2}

Apply radical rule:

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

5^{2} = 5

= 100 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 100 \cdot 10

Multiply the numbers:

100 \cdot 10 = 1000

= 1000

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Frequently Asked Questions (FAQ)

What is sqrt(100^3) ?
The solution to sqrt(100^3) is 1000