Calculation:

Given:
X = 7 + 4√3

To find the value of √X, we substitute the value of X into the expression √X.

So, √X = √(7 + 4√3)

To simplify this expression, we need to rationalize the denominator.

Rationalizing the Denominator:

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of √(7 + 4√3) is √(7 + 4√3).

Multiplying the numerator and denominator by the conjugate, we get:

√X = (√(7 + 4√3) * √(7 - 4√3)) / (√(7 - 4√3) * √(7 - 4√3))

Simplifying this expression, we have:

√X = (√(7 + 4√3) * √(7 - 4√3)) / (7 - 4√3)

Simplifying the Numerator:

To simplify the numerator, we use the product rule for radicals: √a * √b = √(a * b).

√(7 + 4√3) * √(7 - 4√3)

= √[(7 + 4√3) * (7 - 4√3)]

= √[49 - (4√3)^2]

= √[49 - 16 * 3]

= √[49 - 48]

= √1

= 1

Simplifying the Denominator:

The denominator is 7 - 4√3.

Final Calculation:

Now, we can substitute the simplified numerator and denominator back into the expression for √X:

√X = 1 / (7 - 4√3)

So, the value of √X is 1 divided by (7 - 4√3).

Explanation:

We were given the value of X as 7 + 4√3. To find the value of √X, we substituted the value of X into the expression √X. We then rationalized the denominator and simplified the expression. Finally, we found that the value of √X is 1 divided by (7 - 4√3).

7-4√3 is ansWer