Chapter 8: Q. 8.91 (page 796)

Simplify $(3 - 2 \sqrt{5}) (3 + 2 \sqrt{5})$ .

Short Answer

Expert verified

The value is $- 11$ .

Step by step solution

Step 1. Given and explanation

We have $(3 - 2 \sqrt{5}) (3 + 2 \sqrt{5})$ .

We can identify the property of product of conjugates, i.e., $(a + b) (a - b)$ .

We know that $(a + b) (a - b) = {(a)}^{2} - {(b)}^{2}$ .

By applying it, we will get the value.

Step 2. Simplifying and evaluating value.

We have $(3 - 2 \sqrt{5}) (3 + 2 \sqrt{5})$ .

Applying the property $(a + b) (a - b)$ will give us,

role="math" localid="1644766740151" $= (3 - 2 \sqrt{5}) (3 + 2 \sqrt{5}) = {(3)}^{2} - {(2 \sqrt{5})}^{2} = 9 - 20 = - 11$

Thus we get the value as $- 11$ .

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Simplify $(3 - 2 \sqrt{5}) (3 + 2 \sqrt{5})$ .

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Simplifying and evaluating value.

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Simplify $(3 - 2 \sqrt{5}) (3 + 2 \sqrt{5})$ .