What is sqrt(64000) ?

The solution to sqrt(64000) is 80sqrt(10)

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simplify sqrt(64000)

simplify

64000

8010

Decimal Notation

252.98221 \dots

Solution steps

64000

Prime factorization of

64000 : 2^{9} \cdot 5^{3}

= 2^{9} \cdot 5^{3}

Apply exponent rule:

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

2^{9} \cdot 5^{3} = 2^{8} \cdot 2 \cdot 5^{2} \cdot 5

= 2^{8} \cdot 2 \cdot 5^{2} \cdot 5

2^{8} \cdot 2 \cdot 5^{2} \cdot 5 = 2^{8} 5^{2} 2 \cdot 5

= 2^{8} 5^{2} 2 \cdot 5

2^{8} = 16

= 16 5^{2} 2 \cdot 5

Apply radical rule:

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

5^{2} = 5

= 16 \cdot 5 2 \cdot 5

Multiply the numbers:

16 \cdot 5 = 80

= 80 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 8010

\frac{1}{12} - \frac{1}{18}

14 \cdot + 8

\frac{1}{2} + \frac{5}{12}

\frac{25 x ^{4} y ^{2}}{25 x ^{7} y ^{3}}