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Popular >

simplify sqrt(189)

Solution

simplify

189

Solution

321

+1

Decimal Notation

13.74772 \dots

Solution steps

189

Prime factorization of

189 : 3^{3} \cdot 7

= 3^{3} \cdot 7

Apply exponent rule:

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

3^{3} \cdot 7 = 3^{2} \cdot 3 \cdot 7

= 3^{2} \cdot 3 \cdot 7

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

3^{2} \cdot 3 \cdot 7 = 3^{2} 3 \cdot 7

= 3^{2} 3 \cdot 7

Apply radical rule:

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

3^{2} = 3

= 3 3 \cdot 7

Multiply the numbers:

3 \cdot 7 = 21

= 321

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Frequently Asked Questions (FAQ)

What is sqrt(189) ?
The solution to sqrt(189) is 3sqrt(21)