What is 3sqrt(1000) ?

The solution to 3sqrt(1000) is 30sqrt(10)

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simplify 3sqrt(1000)

simplify

31000

3010

Decimal Notation

94.86832 \dots

Solution steps

31000

Prime factorization of

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

= 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

= 3 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

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

Apply radical rule:

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

2^{2} = 2

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

Apply radical rule:

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

5^{2} = 5

= 3 \cdot 2 \cdot 5 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 3 \cdot 1010

Multiply the numbers:

3 \cdot 10 = 30

= 3010

(- \frac{1}{2})^{3}

2 x + 8 = 12

(\frac{y}{2})^{- 5}

4 - (- 2)^{2}

x^{4} + 27 x