Question

simplify( 3 root 5 minus 5 root 2)( 4 root 5 + 3 root 2)​

Answer 1

$\Huge{\red{\underline{\textsf{Answer}}}}$

⎇ (3√5-5√2)(4√5+3√2)

⎇ 3√5×4√5+3√5×3√2-5√2×4√5-5√2×3√2

⎇ 12×5+9√10-20√10-15×2

⎇ 60-11√10-30

$30 - 11 \sqrt{10}$

Answer 2

Answer:

(3√5- 5√2)(4√5 +3√2) = 30 - 11√10

Step-by-step explanation:

Required to simplify the expression

(3√5- 5√2)(4√5 +3√2)

Recall the property

The set of irrational numbers is distributive under multiplication over addition

That is if a,b,c are any three irrational numbers, then

a(b+c) = ab+ac

Solution

We have the expression (3√5- 5√2)(4√5 +3√2)

Applying the distributive property we get

3√5(4√5 +3√2) - 5√2(4√5 +3√2)

Again applying the distributive property we get

= 3√5×4√5 +3√5×3√2 - 5√2 ×4√5 - 5√2 ×3√2

= 12 ×5 + 9×√5×√2 - 20×√2 ×√5 - 15×2

= 60 + 9√10 - 20√10 - 30

= 30 - 11√10

∴(3√5- 5√2)(4√5 +3√2) = 30 - 11√10

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