State whether the following statement is TRUE or FALSE.
$(2 - \sqrt{3})^{2}$ is irrational.

Question

State whether the following statement is or FALSE-2-sqrt-3-2- is irrational-TrueFalse

Toppr Admin · Accepted Answer

Formula-a-x2212-b-2-a2-b2-x2212-2abApplying-xA0-the formula- we get -2-x2212-x221A-3-2-22-x221A-32-x2212-2-xD7-2-xD7-x221A-3-4-3-x2212-4-x221A-3-7-x2212-4-x221A-37-x2212-4-x221A-3 is an irrational number-x27F9-2-x2212-x221A-3-2 is an irrational number-

State whether the following statement is TRUE or FALSE.
$(2 - \sqrt{3})^{2}$ is irrational.

True
False

Formula
${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$

Applying the formula, we get
${(2 - \sqrt{3})}^{2} = 2^{2} + {\sqrt{3}}^{2} - 2 \times 2 \times \sqrt{3} = 4 + 3 - 4 \sqrt{3} = 7 - 4 \sqrt{3}$

$7 - 4 \sqrt{3}$ is an irrational number.

$⟹ {(2 - \sqrt{3})}^{2}$ is an irrational number.

State whether the following statement is TRUE or FALSE.(2−√3)2 is irrational.TrueFalse

Formula(a−b)2=a2+b2−2abApplying the formula, we get (2−√3)2=22+√32−2×2×√3=4+3−4√3=7−4√37−4√3 is an irrational number.⟹(2−√3)2 is an irrational number.

State whether the following statement is TRUE or FALSE.
$(2 - \sqrt{3})^{2}$ is irrational.

True
False

Formula
${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$

Applying the formula, we get
${(2 - \sqrt{3})}^{2} = 2^{2} + {\sqrt{3}}^{2} - 2 \times 2 \times \sqrt{3} = 4 + 3 - 4 \sqrt{3} = 7 - 4 \sqrt{3}$

$7 - 4 \sqrt{3}$ is an irrational number.

$⟹ {(2 - \sqrt{3})}^{2}$ is an irrational number.