Question

Solve the question
$\sqrt{63} - 5 \sqrt{2p} + 11 \sqrt{7}$
​

Answer 1

⠀⠀$\huge\underline{ \underline{ \bf{ \blue{ \: solution \: : = }}}}$

$\sqrt{63} - 5 \sqrt{2p} + 11 \sqrt{7}$

$\bf \:3 \sqrt{7} - 5 \sqrt{2p} + 11 \sqrt{7} \\ \\ 14 \sqrt{7} - 5 \sqrt{2p}$

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SOLVE FOR P

Steps for Solving Linear Equation

⠀⠀⟹$\sqrt { 63 } - 5 \sqrt { 2 } p + 11 \sqrt { 7 } = 0$

view step

$63=3^{2}\times 7$

$\sqrt{3^{2}\times 7}=\sqrt{63}</p><p>$

$\sqrt{3^{2}}\sqrt{7} = \sqrt{63}$

$3^{2}\approx 9$

⠀⠀➠$3\sqrt{7}-5\sqrt{2}p+11\sqrt{7}=0$

⠀⠀➠$</p><p>3\sqrt{7}-5\sqrt{2}p=-11\sqrt{7}$

⠀⠀➠$-5\sqrt{2}p=-11\sqrt{7}-3\sqrt{7}$

⠀⠀➠$\left(-5\sqrt{2}\right)p=-14\sqrt{7}</p><p>$

⠀⠀➠$\frac{\left(-5\sqrt{2}\right)p}{-5\sqrt{2}}=-\frac{14\sqrt{7}}{-5\sqrt{2}} =$

⠀⠀➠$p=-\frac{14\sqrt{7}}{-5\sqrt{2}}$

⠀⠀⠀➠${\boxed{\fbox{\green{\bf{p=\frac{7\sqrt{14}}{5}}}}}}$

Answer 2

Correct Question :

$\sf \: \sqrt{63} - 5 \sqrt{28} + 11 \sqrt{7}$

Solution :

For solving these kind of questions,you need to bring all of them in their simple form.

We can write :

$\star \sf \: \sqrt{63} \: \: as \: \: \: \sqrt{9 \times 7}$

$\star \sf \: \sqrt{28} \: \: as \: \: \: \sqrt{4 \times 7}$

Let's put the value :

$\sf \: \longmapsto \: \sqrt{9 \times 7} - 5 \sqrt{4 \times 7} + 11 \sqrt{7}$

We know that :

$\star \sf \: \sqrt{9} \: \: = 3$

$\star \sf \: \sqrt{4} \: \: = 2$

Let's put the value :

$\sf \longmapsto 3 \sqrt{7} - 5(2) \sqrt{7} + 11 \sqrt{7}$

$\sf \: \longmapsto \: 3 \sqrt{7} - 10 \sqrt{7} + 11 \sqrt{7}$

Here,√7 is common. Let's take this out

$\sf \: \longmapsto \: (3 - 10 + 11) \sqrt{7}$

We can add all those numbers except √7

$\longmapsto \sf \:(14 - 10)\sqrt{7}$

$\longmapsto \large \boxed{ \purple{ \sf \: 4 \sqrt{7}} }$

Hence,Required Value is 4√7