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Popular >

simplify sqrt(1800)

Solution

simplify

1800

Solution

302

+1

Decimal Notation

42.42640 \dots

Solution steps

1800

Prime factorization of

1800 : 2^{3} \cdot 3^{2} \cdot 5^{2}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

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

Apply radical rule:

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

3^{2} = 3

= 22 \cdot 3 5^{2}

Apply radical rule:

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

5^{2} = 5

= 22 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 302

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Frequently Asked Questions (FAQ)

What is sqrt(1800) ?
The solution to sqrt(1800) is 30sqrt(2)