Question

How do you evaluate 4√112 +5√56 - 9√126?

Answer 1

Answer : -21.27615

Step by step explanation :

$4 \sqrt{112} + 5 \sqrt{56} - 9 \sqrt{126}$

Simplify the roots.

Factor out the perfect square.

$= > 4 \sqrt{4 {}^{2} \times 7} + 5 \sqrt{56} - 9 \sqrt{126}$

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

$= > 4 \sqrt{4 {}^{2} } \sqrt{7} + 5 \sqrt{56} - 9 \sqrt{126}$

Reduce the index of the radical and exponent with 2

$= > 4 \times 4 \sqrt{7} + 5 \sqrt{56} - 9 \sqrt{126}$

Calculate the product

$= > 16 \sqrt{7} + 5 \sqrt{56} - 9 \sqrt{126}$

Simplify the radicle. Factor out the perfect square.

$= > 16 \sqrt{7} + 5 \sqrt{2 {}^{2} \times 14 } - 9 \sqrt{126}$

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

$= > 16 \sqrt{7} + 5 \sqrt{2 {}^{2} } \sqrt{14} - 9 \sqrt{126}$

Reduce the index of the radical and exponent with 2

$= > 16 \sqrt{7} + 5 \times 2 \sqrt{14} - 9 \sqrt{126}$

Calculate the product

$= > 16 \sqrt{7} + 10 \sqrt{14} - 9 \sqrt{126}$

Simplify the radicle. Factor out the perfect square

$= > 16 \sqrt{7} + 10 \sqrt{14} - 9 \sqrt{3 {}^{2} \times 14 }$

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

$= > 16 \sqrt{7 } + 10 \sqrt{14} - 9 \sqrt{3 {}^{2} } \sqrt{14}$

Reduce the index of the radical and exponent with 2.

$= >16 \sqrt{7} + 10 \sqrt{14} - 9 \times 3 \sqrt{14}$

Calculate the product.

$= > 16 \sqrt{7} + 10 \sqrt{14} - 27 \sqrt{14}$

Collect the like terms by subtracting their coefficients

$= > 16 \sqrt{7} (10 - 27) \sqrt{14}$

Calculate the difference

$= > 16 \sqrt{7} - 17 \sqrt{14}$

$= > - 21.27615$