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Popular >

simplify 200^{1/2}

Solution

simplify

20 0^{\frac{1}{2}}

Solution

10 \cdot 2^{\frac{1}{2}}

+1

Decimal Notation

14.14213 \dots

Solution steps

20 0^{\frac{1}{2}}

Prime factorization of

200 : 2^{3} \cdot 5^{2}

= (2^{3} \cdot 5^{2})^{\frac{1}{2}}

Apply exponent rule:

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

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

= (2^{2} \cdot 2 \cdot 5^{2})^{\frac{1}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2^{2} \cdot 2 \cdot 5^{2})^{\frac{1}{2}} = (2^{2})^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} (5^{2})^{\frac{1}{2}}

= (2^{2})^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} (5^{2})^{\frac{1}{2}}

(2^{2})^{\frac{1}{2}} = 2

= 2 \cdot 2^{\frac{1}{2}} (5^{2})^{\frac{1}{2}}

(5^{2})^{\frac{1}{2}} = 5

= 2 \cdot 2^{\frac{1}{2}} \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10 \cdot 2^{\frac{1}{2}}

Popular Examples

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∣ 2 x - 5 ∣ < ∣ 3 x - 2 ∣

Frequently Asked Questions (FAQ)

What is 200^{1/2} ?
The solution to 200^{1/2} is 10*2^{1/2}