Question

please tell it to me with detailed explanation​

Answer 1

Question:

If $\sf\:\sqrt{2}\:=\:1.414\:\&\:\sqrt{3}\:=\:1.732$, then find the value of $\sf\:\dfrac{4}{3\:\sqrt{3}\:-\:2\:\sqrt{2}}\:+\:\dfrac{3}{3\:\sqrt{3}\:+\:2\:\sqrt{2}}$

Answer:

The value of

$\boxed{\red{\sf\:\dfrac{4}{3\:\sqrt{3}\:-\:2\:\sqrt{2}}\:+\:\dfrac{3}{3\:\sqrt{3}\:+\:2\:\sqrt{2}}\:=\:2.06}}$ (Approx.)

Step-by-step-explanation:

NOTE: Kindly refer to the attachment for the steps.

To solve the given question, we have to follow the following steps.

1. Multiply both the numerator and denominator of both the fractions by the conjugate pair of the denominator.

2. The numerator will be perfect i. e. there will be no operations performed.

3. In denominator, use an algebraic identity i. e. ( a + b ) ( a - b ) = a² - b².

4. Solve the denominator using the identity and multiplication.

5. The denominator will be rationalised.

6. Both fractions have the same denominator and hence they both will be added.

7. Collect the like terms from the numerator and perform the necessary operations i. e. addition and subtraction.

8. Substitute the given values of $\sf\:\sqrt{2}\:\&\:\sqrt{3}$ in the obtained fraction.

9. Solve the numerator and get the addition.

10. Perform the division of numerator and denominator to get the approx value of the given two fractions.