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Popular >

simplify sqrt(1400)

Solution

simplify

1400

Solution

1014

+1

Decimal Notation

37.41657 \dots

Solution steps

1400

Prime factorization of

1400 : 2^{3} \cdot 5^{2} \cdot 7

= 2^{3} \cdot 5^{2} \cdot 7

Apply exponent rule:

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

2^{3} \cdot 5^{2} \cdot 7 = 2^{2} \cdot 2 \cdot 5^{2} \cdot 7

= 2^{2} \cdot 2 \cdot 5^{2} \cdot 7

2^{2} \cdot 2 \cdot 5^{2} \cdot 7 = 2^{2} 5^{2} 2 \cdot 7

= 2^{2} 5^{2} 2 \cdot 7

Apply radical rule:

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

2^{2} = 2

= 2 5^{2} 2 \cdot 7

Apply radical rule:

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

5^{2} = 5

= 2 \cdot 5 2 \cdot 7

Multiply the numbers:

2 \cdot 5 = 10

= 10 2 \cdot 7

Multiply the numbers:

2 \cdot 7 = 14

= 1014

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Frequently Asked Questions (FAQ)

What is sqrt(1400) ?
The solution to sqrt(1400) is 10sqrt(14)