Question

solve the question
(3-2√2)^2​

Answer 1

Answer:

(3-2√2)^2

= by using identity (a-b)^2=a^2+b^2-2ab

=(3)^2+(2√2)^2-2(3)(2√2)

=9+8-24√2

=17-24√2

Answer 2

Answer:

$\Large\boxed{17-12\sqrt{2} }$

Step-by-step explanation:

GIVEN:

(3-2√2)²

To solve this problem, first you have to use perfect square formula.

SOLUTIONS:

First, you have to use perfect square formula from left to right numbers.

$\Large\boxed{\textnormal{PERFECT SQUARE FORMULA}}$

$\displaystyle (A-B)^2=A^2-2AB+B^2$

A=3

B=2√2

Rewrite the whole problem down.

$\displaystyle 3^2-2*3*2\sqrt{2}+(2\sqrt{2})^2$

Solve.

$\displaystyle 3^2=3*3=9$

$\displaystyle 2*3*2=12$

$\displaystyle 12\sqrt{2}$

$\displaystyle 2^2=2*2=4$

$\displaystyle 4*2=8$

Used exponent rule.

$\Large\boxed{\textnormal{EXPONENT RULES}}$

$\displaystyle A^B*A^C=A^B^+^C$

$\displaystyle 2^2*2=2^2^+^1$

Add.

$\displaystyle 2+1=3$

$\displaystyle 2^3=2*2*2=8$

Rewrite the whole problem down.

$\displaystyle 9-12\sqrt{2}+8$

Add.

$\displaystyle 8+9=\boxed{17}$

$\Large\boxed{17-12\sqrt{2}}}$

Therefore, the correct answer is 17-12√2.