Question

How do you simplify 2√52√7+3√3?

Answer 1

Answer : 43.35372

Step by step explanation :

$2 \sqrt{52} \sqrt{7} + 3 \sqrt{3}$

Simplify the radicle √52.

Factor out the perfect square.

$= > 2 \times 2 \sqrt{2 {}^{2} \times 13} \sqrt{7} + 3 \sqrt{3}$

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

$= > 2 \times 2\sqrt{2 {}^{2} } \sqrt{13} \sqrt{7} + 3 \sqrt{3}$

Reduce the index of the radical and exponent with 2.

$= > 2 \times 2 \sqrt{13} \sqrt{7} + 3 \sqrt{3}$

Calculate the product by multiplying the numbers.

$= > 4 \sqrt{13} \sqrt{7} + 3 \sqrt{3}$

The product of roots with the same index is equal to the root of the product.

$= > 4 \sqrt{13 \times 7} + 3 \sqrt{3}$

Multiply the numbers.

$= > 4 \sqrt{91} + 3 \sqrt{3}$