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Popular >

simplify sqrt(45000)

Solution

simplify

45000

Solution

1502

+1

Decimal Notation

212.13203 \dots

Solution steps

45000

Prime factorization of

45000 : 2^{3} \cdot 3^{2} \cdot 5^{4}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

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

Apply radical rule:

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

3^{2} = 3

= 22 \cdot 3 5^{4}

5^{4} = 25

= 22 \cdot 3 \cdot 25

Multiply the numbers:

2 \cdot 3 \cdot 25 = 150

= 1502

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Frequently Asked Questions (FAQ)

What is sqrt(45000) ?
The solution to sqrt(45000) is 150sqrt(2)