What is 5sqrt((32)(243)) ?

The solution to 5sqrt((32)(243)) is 180sqrt(6)

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simplify 5sqrt((32)(243))

simplify

5 (32) (243)

1806

Decimal Notation

440.90815 \dots

Solution steps

5 (32) (243)

(32) (243) = 32 \cdot 243

= 5 32 \cdot 243

Multiply the numbers:

32 \cdot 243 = 7776

= 57776

Prime factorization of

7776 : 2^{5} \cdot 3^{5}

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

Apply exponent rule:

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

2^{5} \cdot 3^{5} = 2^{4} \cdot 2 \cdot 3^{4} \cdot 3

= 5 2^{4} \cdot 2 \cdot 3^{4} \cdot 3

2^{4} \cdot 2 \cdot 3^{4} \cdot 3 = 2^{4} 3^{4} 2 \cdot 3

= 5 2^{4} 3^{4} 2 \cdot 3

2^{4} = 4

= 5 \cdot 4 3^{4} 2 \cdot 3

3^{4} = 9

= 5 \cdot 4 \cdot 9 2 \cdot 3

Multiply the numbers:

4 \cdot 9 = 36

= 5 \cdot 36 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 5 \cdot 366

Multiply the numbers:

5 \cdot 36 = 180

= 1806

(\frac{2}{3}) (\frac{3}{5})

(x + 7) (x - 10)

lo g_{2} (2^{10})

(4 t - x) (t - x + 1)

9 + 25