The square root of 33-4√35 is

Correct option is D

1. Given:

​$$\sqrt{33 - 4\sqrt{35}}$$​​

2. Formula Used:

If $$\sqrt{a - 2\sqrt{b}}$$​ can be expressed as $$\sqrt{x} - \sqrt{y}$$​, then:

x + y = a

​$$2\sqrt{xy} = 2\sqrt{b}$$​​

3. Solution:

- Let:

​$$\sqrt{33 - 4\sqrt{35}} = \sqrt{x} - \sqrt{y}$$​​

- Using the formula:

1. x + y = 33

2. $$2\sqrt{xy} = 4\sqrt{35}, so \sqrt{xy} = 2\sqrt{35}$$​, which implies xy = $$4 \times 35$$​ = 140.

- Solve x and y using the equations:

- x + y = 33

- xy = 140

- These are roots of the quadratic equation:

​$$t^2 - 33t + 140 = 0$$​​

- Solve the quadratic equation:

​$$t = \frac{33 \pm \sqrt{33^2 - 4 \cdot 1 \cdot 140}}{2}$$​​

​$$t = \frac{33 \pm \sqrt{1089 - 560}}{2}$$​​

​$$t = \frac{33 \pm \sqrt{529}}{2}$$​​

t = \frac{33 \pm 23}{2}

​$$t = 28 \quad \text{or} \quad t = 5$$​​

- Therefore, x = 28 and y = 5.

- The expression becomes:

​$$\sqrt{33 - 4\sqrt{35}} = \sqrt{28} - \sqrt{5}$$

$$2\sqrt{7} - \sqrt{5}$$​​​