Question

$\sqrt{34+24\sqrt{2} } * 4-3\sqrt{2}$

Answer 1

$\sqrt{34+24\sqrt{2} } \times 4-3\sqrt{2}$

$\sqrt{34 + 24 \sqrt{2} }$

Can be Written as

$=34 + 24 \sqrt{2} \\ \\ = 16 + 18 + 24 \sqrt{2} \\ \\ = {4}^{2} + ( 3 \sqrt{2}) {}^{2} + 24 \sqrt{2} \\ \\ = {4}^{2} + (3 \sqrt{2} ) {}^{2} + 2 \times 4 \times 3 \sqrt{2}$

As we know

$(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab$

${4}^{2} + (3 \sqrt{2} ) {}^{2} + 2 \times 4 \times 3 \sqrt{2} \\ \\ = (4 + 3 \sqrt{2} ) {}^{2}$

It was Underoot

$\sqrt{(4 + 3 \sqrt{2} ) {}^{2} } \\ \\ (4 + 3 \sqrt{2} ) {}^{2 \times \frac{1}{2} } \\ \\ 4 + 3 \sqrt{2}$

Now We have to Multiply it with

4-3√2

$(4 + 3 \sqrt{2} )(4 - 3 \sqrt{2} ) \\ \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ \\ {4}^{2} - (3 \sqrt{2}) {}^{2} \\ \\ 16 - 9 \times 2 \\ \\ 16 - 18 \\ \\ = - 2$

$\boxed{\mathbf{\huge{Answer=-2}}}$