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Popular >

simplify sqrt(1000)

Solution

simplify

1000

Solution

1010

+1

Decimal Notation

31.62277 \dots

Solution steps

1000

Prime factorization of

1000 : 2^{3} \cdot 5^{3}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

= 2 5^{2} 2 \cdot 5

Apply radical rule:

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

5^{2} = 5

= 2 \cdot 5 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 1010

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Frequently Asked Questions (FAQ)

What is sqrt(1000) ?
The solution to sqrt(1000) is 10sqrt(10)