Problem:
Find the value of 6/√5 - √3 if √3=1.732 and √5=2.236.

Solution:

To find the value of the given expression, we can substitute the values of √3 and √5 into the expression and evaluate it.

Step 1: Substituting the values
Substitute the values of √3 and √5 into the expression:
6/√5 - √3

Replacing √3 with 1.732 and √5 with 2.236, the expression becomes:
6/2.236 - 1.732

Step 2: Simplifying the expression
To simplify the expression, we need to find a common denominator for the two terms.

Term 1: 6/2.236
The denominator can be rationalized by multiplying both the numerator and denominator by the conjugate of 2.236, which is 2.236 - 0:

6/2.236 = (6 * (2.236 - 0))/(2.236 * (2.236 - 0))
= (13.416 - 0)/(5)
= 13.416/5
= 2.6832

Term 2: 1.732

Step 3: Evaluating the expression
Now that we have simplified the expression, we can evaluate it by subtracting term 2 from term 1:

2.6832 - 1.732 = 0.9512

Therefore, the value of 6/√5 - √3, when √3=1.732 and √5=2.236, is 0.9512.

Summary:
- The value of 6/√5 - √3 is 0.9512.
- The expression was simplified by rationalizing the denominator of the first term.
- The values of √3 and √5 were substituted into the expression to evaluate it.

First rationalise it
6/root 5 - root 3 × root 5 + root3/root 3 + root 5
6 (root 3 + root 5)/2
6 (1.732+2.236)/2
3 ( 3.968)
11.904