Question

Simplify
a) (√5-3)(√5+3)
b) (3√2+√3)^2

Answer 1

Step-by-step explanation:

a. by id a^2 - b^2 = 5 -9 = -4

b. 9 ×2 + 3 + 2 × 3 × √6

= 21 +6√6

Answer 2

Answer:

$\boxed{1.) -4}$

$\boxed{2.)21 + \sqrt[6]{6}}$

Step-by-step explanation:

In this first sum,

$( \sqrt{5} - 3)( \sqrt{5} + 3) \\ \sqrt{5} ( \sqrt{5} + 3) - 3( \sqrt{5} + 3) \\ 5 + \sqrt[3]{5} - \sqrt[3]{5} - 9 \\→ - 4$

Extra :

• Here, you can also use the identity : a² - b² = (a+b) (a-b)

In the second sum,

$( { \sqrt[3]{2} + \sqrt{3} })^{2} = ( { \sqrt[3]{2} + \sqrt{3} })( \sqrt[3]{2} + \sqrt{3} ) \\ \sqrt[3]{2} ( \sqrt[3]{2} + \sqrt{3} ) + \sqrt{3} ( \sqrt[3]{2} + \sqrt{3} ) \\ 18 + \sqrt[3]{6} + \sqrt[3]{6} + 3 \\→ 21 + \sqrt[6]{6}$

Extra :

• Here, you can also use the identity : (a+b)² = a² + b² + 2ab

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