Courses
Courses for Kids
Free study material
Offline Centres
More
Store

The value of the expression $\sqrt {34 + 24\sqrt 2 } \times \left( {4 - 3\sqrt 2 } \right)$ is?A.$- 4$B.$- 2$C.3D.4

Last updated date: 11th Jun 2024
Total views: 401.4k
Views today: 12.01k
Verified
401.4k+ views
Hint: Here, we will rewrite the given equation by using the rule ${a^2} + 2ab + {b^2} = {\left( {a + b} \right)^2}$ and
${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$. Then simplify the obtained equation to find the required value.

We are given that $\sqrt {34 + 24\sqrt 2 } \times \left( {4 - 3\sqrt 2 } \right)$.
Rewriting the given equation, we get
$\Rightarrow \sqrt {16 + 18 + 2 \cdot 4 \cdot 3\sqrt 2 } \times \left( {4 - 3\sqrt 2 } \right) \\ \Rightarrow \sqrt {{4^2} + {{\left( {3\sqrt 2 } \right)}^2} + 2 \cdot 4 \cdot 3\sqrt 2 } \times \left( {4 - 3\sqrt 2 } \right) \\$
Using the rule,${a^2} + 2ab + {b^2} = {\left( {a + b} \right)^2}$ in the above equation, we get
$\Rightarrow \sqrt {{{\left( {4 + 3\sqrt 2 } \right)}^2}} \times \left( {4 - 3\sqrt 2 } \right) \\ \Rightarrow \left( {4 + 3\sqrt 2 } \right) \times \left( {4 - 3\sqrt 2 } \right) \\$
Using the rule,${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$ in the above equation, we get
$\Rightarrow {4^2} - {\left( {3\sqrt 2 } \right)^2} \\ \Rightarrow 16 - 18 \\ \Rightarrow - 2 \\$
Thus, the required value is $- 2$.
Hence, option B is the correct answer.

Note: In this question, students should know that a square root of a number is a value that, when multiplied by itself, gives the number. This is a really simple problem, basic knowledge about the trigonometric is enough. We need to know that when $\sqrt 2$ is multiplied with itself is equal to 2.