Question

Ratinalise the denominator of .1/√3-√2

help for my online exam​

Answer 1

Answer:

Rationalise the denominator of 1/√3+√2 and hence evaluate by taking √2 = 1.414 and √3 = 1.732,up to three places of decimal.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Consider √2 + √3 as a single term and √4 or 2 as another term

So

1 ÷ [ (√2+√3)-(2) ]

Now do what we normally do for 1÷ a-b

We multiply it by a+b in both numerator and denominator

Do the same here

Multiply (√2+√3)+2 on both numerator and denominator

{ 1×[(√2+√3)+2] } ÷ [(√2+√3)-2]×[(√2+√3)+2]

As we know that (a+b)×(a-b) = a²-b²

= (√2+√3+2) ÷ (√2+√3)²-2²

We know that (a+b)² = a² + b² +2ab so

= (√2+√3+2) ÷ (√2)²+(√3)²+2×√2×√3- 4

= (√2+√3+2) ÷ 2 + 3+ 2√6 -4

= (√2+√3+2) ÷ 5–4 + 2√6

= (√2 +√3 + 2) ÷ 1+2√6

Now rationalise this by multiplying 1–2√6 on both numerator and denominator

=[(√2+√3+2)× (1-2√6)] ÷ [(1+2√6)×(1–2√6)]

=[(√2+√3+2)×(1–2√6)]÷[1²-(2√6)²]

As (2√6)²=[2²×(√6)²]=(4×6)=24

=[(√2+√3+2)×(1–2√6)]÷[1–24]

=[(√2+√3+2)×(1–2√6)]÷(-23)

Now take - (minus) sign upwards

= — [(√2+√3+2)×(1–2√6)] ÷23