Question

2 s square minus (1 + 2 under root 2) 5 + under root 2​

Answer 1

Answer:

Sol: We know that (√a+√b)2 = a+b+2√ab

Now √(5 + 2√6). If it is a perfect sq, there will be 2 no.s - such that a + b = 5.

2√ab = 2√6 ⇒ ab = 6      (a=3, b=2)

so that, 5 + 2√6 = 3+2+2√(3×2)

                         =(√3+√2)2

∴ √( 5 + 2√6) = √3+√2.

similarly, Consider √(8 - 2√15)

a + b = 8 ⇒ ab = 15 (a = 5,b = 3)

√(8 - 2√15) = (√5 - √3)

Now √( 5 + 2√6) + √(8 - 2√15) = √3 + √2 + √5 - √3 = √2 + √5.

Step-by-step explanation:

Answer 2

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$= {2}^{2} (1 - 2 \sqrt{2} ) + \sqrt{2}$

$= 4(1 - 2 \sqrt{2} ) + \sqrt{2}$

$= 4 - 8 \sqrt{2} + \sqrt{2}$

$= 4 - 7 \sqrt{2}$