Question

2√15× 3√32× 4√18 simplify​

Answer 1

Answer : 2230.83841

Step by step explanation :

$2 \sqrt{15} \times 3 \sqrt{32} \times 4 \sqrt{18}$

Simplify the roots.

Factor out the perfect square.

$= > 2 \sqrt{15} \times 3 \sqrt{4 {}^{2} \times 2 } \times 4 \sqrt{3 {}^{2} \times 2}$

The root of a product is equal to the product of the roots of each factor.

$= > 2 \sqrt{15} \times 3 \sqrt{4 {}^{2} } \sqrt{2} \times 4 \times \sqrt{3 {}^{2} } \sqrt{2}$

Reduce the index of the radical and exponent with 2.

$= > 2 \sqrt{15} \times 3 \times 4 \sqrt{2} \times 4 \times 3 \sqrt{2}$

When an square root of an expression is multiplied by itself, the result is that expression.

$= > 2 \sqrt{15} \times 3 \times 4 \times 2 \times 4 \times 3$

Write the repeated multiplication in exponential form.

$= > 2 {}^{2} \times \sqrt{15} \times 3 {}^{2} \times 4 {}^{2}$

Evaluate the power.

$= > 4 \sqrt{15} \times 9 \times 16$

Multiply the numbers.

$= > 36 \sqrt{15} \times 16$

Multiply the numbers

$= > 576 \sqrt{15}$

$= > 2230.83841$