Question

given that 8-sqrt(18) over sqrt(2) = a + b sqrt(2) where a and b are integers find the value of a and b

Answer 1

Answer:

a = - 3 and b = 4

Step-by-step explanation:

Given

$\frac{8-\sqrt{18} }{\sqrt{2} }$

Simplify $\sqrt{18}$

= $\sqrt{9(2)}$ = $\sqrt{9}$ × $\sqrt{2}$ = 3$\sqrt{2}$

Thus expression can be written as

$\frac{8-3\sqrt{2} }{\sqrt{2} }$

Multiply numerator/denominator by $\sqrt{2}$

noting that $\sqrt{2}$ × $\sqrt{2}$ = 2

= $\frac{\sqrt{2}(8-3\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }$

= $\frac{8\sqrt{2}-6 }{2}$

Dividing each term on the numerator by 2

= 4$\sqrt{2}$ - 3

= - 3 + 4$\sqrt{2}$

with a = - 3 and b = 4

Answer 2

Answer:

a = -3, b = 4.

Step-by-step explanation:

(8 - √18) / √2

= (8 - 3√2) √2

= 8/√2  - 3

=  8√2 / 2 - 3

= -3 + 4√2

So  a + b√2 = -3 + 4√2

Comparing coefficients we have:

a = -3 and b = 4 (answer).