What is sqrt(81m^5n^2-9m^6n^5) ?

The solution to sqrt(81m^5n^2-9m^6n^5) is 3m^2nsqrt(m)sqrt(9-mn^3)

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simplify sqrt(81m^5n^2-9m^6n^5)

simplify

81 m^{5} n^{2} - 9 m^{6} n^{5}

3 m^{2} n m 9 - m n^{3}

Solution steps

81 m^{5} n^{2} - 9 m^{6} n^{5}

Factor out common term

9 m^{5} n^{2} : 9 m^{5} n^{2} (9 - m n^{3})

= 9 m^{5} n^{2} (9 - m n^{3})

9 m^{5} n^{2} (9 - m n^{3}) = 9 m^{5} n^{2} 9 - m n^{3}

= 9 m^{5} n^{2} 9 - m n^{3}

9 = 3

= 3 m^{5} n^{2} 9 - m n^{3}

Simplify

m^{5} : m^{2} m

= 3 m^{2} m n^{2} 9 - m n^{3}

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

n^{2} = n

= 3 m^{2} m n 9 - m n^{3}

= 3 m^{2} n m 9 - m n^{3}

1 0^{2} + 1 0^{2} + 5^{2}

7 a + 8 a^{2} + 7 a^{0} - 4 a^{2} - 9 a

(4 + 4 i)^{2}

5 x^{2} + 10 x + 10

- 8 \frac{3}{5} \div 1 \frac{1}{5}

What is sqrt(81m^5n^2-9m^6n^5) ?
The solution to sqrt(81m^5n^2-9m^6n^5) is 3m^2nsqrt(m)sqrt(9-mn^3)