Question

given that
10 - √18
—————
√2
= a + b √2 where a and b are integers.
Find the values of a and b.

Answer 1

Answer:

a = -3

b = 5

Step-by-step explanation:

$\frac{10-\sqrt{18}}{\sqrt{2}}$

Simplify the square root of 18.

$\frac{10-3\sqrt{2}}{\sqrt{2}}$

Rationalize the fraction.

$\frac{\left(10-3\sqrt{2}\right)\sqrt{2}}{\sqrt{2}\sqrt{2}}$

$\frac{2\left(5\sqrt{2}-3\right)}{2}$

$5\sqrt{2}-3$

Rewrite the answer in the form a+b√2.

$-3 + 5\sqrt{2}$

Answer 2

The given form of expression a + b √2 where a and b are integers then the values of a and b are -3 and 5.

What is factorization?

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

$\frac{10 -\sqrt18} {\sqrt 2}= a + b \sqrt 2$

Simplify the square root of 18 then Rationalize the fraction,

$\\\frac{10 -3\sqrt2} {\sqrt 2}\\\\\frac{(10 -3\sqrt2) \times \sqrt{2} } {\sqrt 2 \sqrt 2}\\\\\frac{ 2(5\sqrt2 -3) } { 2}\\\\(5\sqrt2 -3)$

Thus, the values of a and b are -3 and 5.

Learn more about factors;

https://brainly.com/question/24182713