Question

Find the value of (√a + √b) (√a – √b) is *
(a) a + b
(b) a – b
(c) 2√a
(d) 2√b​

Answer 1

Required Answer:-

Here in this question we are provided with a equation and we are supposed to calculate the value of that equation, such that,

• (√a + √b) (√a – √b)

Now, let's solve the equation a nd understanding the steps to get our final answer.

➝ (√a + √b) (√a – √b)

Expand the expression/equation by using (a - b) (a + b) = a² - b²,

➝ (√a)² - (√b)²

Calculate the power of (√a)² from the expression/equation,

➝ a - (√b)²

Calculate the power of (√b)² also Same as (√a)² from the expression/equation,

➝ a - b

Therefore, the value of the equation is a - b. So (b) a - b is the correct option for this question.[tex][/tex]

Answer 2

Given

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• An equation i.e, (√a + √b) (√a – √b).

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To Find

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• Value of (√a + √b) (√a – √b) ?

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Given Options

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• (a) a + b

• (b) a – b

• (c) 2√a

• (d) 2√b

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Answer

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• Option (b) a – b is correct ☑

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Step – by – step explanation

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$\qquad\tiny\bf{\dag}\:\underline{\frak{We\:know\:that\:::}}$

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$\quad\odot\:{\underline{\boxed{\bf{\blue{(A + B)\:(A - B) = A^2 - B^2}}}}}$

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$\qquad\tiny\bf{\dag}\:\underline{\frak{Using\:this\:identity\:on\:given\:equation\:::}}$

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We have ::

• A = √a

• B = √b

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$\qquad\tiny\bf{\dag}\:\underline{\frak{Putting\:all\:known\:values\:::}}$

$\\ \dashrightarrow\: \footnotesize\sf \big(\sqrt{a} + \sqrt{b}\big)\:\big(\sqrt{a} - \sqrt{b}\big) = \big(\sqrt{a}\big)^2 - \big(\sqrt{b}\big)^2$

$\\ \dashrightarrow\: \footnotesize\boxed{\frak{\green{ \big(\sqrt{a} + \sqrt{b}\big)\:\big(\sqrt{a} - \sqrt{b}\big) = a - b}}}\:\pink{\bigstar}$

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Therefore, value of (√a + √b) (√a – √b) is a – b. So, option (b) a – b is correct ☑

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More to know

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$\boxed{\begin{array}{c} \\ \tiny\bf{\dag}\:\underline{\frak{\rm{S}\frak{ome\:important\:algebric\:identities\:::}}} \\\\ \green{\bigstar}\:\rm \red{ (A+B)^{2} = A^{2} + 2AB + B^{2}} \\\\ \red{\bigstar}\rm\: \green{(A-B)^{2} = A^{2} - 2AB + B^{2}} \\\\ \orange{\bigstar}\rm\: \blue{A^{2} - B^{2} = (A+B)(A-B)}\\\\ \blue{\bigstar}\rm\: \orange{(A+B)^{2} = (A-B)^{2} + 4AB}\\\\ \pink{\bigstar}\rm\: \purple{(A-B)^{2} = (A+B)^{2} - 4AB}\\\\ \purple{\bigstar} \rm\: \pink{(A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}}\\\\ \gray{\bigstar}\rm\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\ \bigstar\rm\: \gray{A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})} \\\\ \end{array}}$

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