Question

The question is in the pic
plz answer it fast

Answer 1

GIVEN :–

$\\ \bf \: \to \: \sqrt{x} = 20$

$\\ \bf \: \to \: \sqrt{x} .\sqrt{y} = 50 \sqrt{z}$

$\\ \bf \: \to \: \sqrt{x} .\sqrt{y} .\sqrt{z} = 200$

TO FIND :–

• Value of $\bf\sqrt{x} + \sqrt{y} + \sqrt{z} = ?$

SOLUTION :–

$\\ \bf \: \to \: \sqrt{x} = 20 \: \: \: \: \: - - - eq.(1)$

$\\ \bf \: \to \: \sqrt{x} .\sqrt{y} = 50 \sqrt{z} \: \: \: \: \: - - - eq.(2)$

$\\ \bf \: \to \: \sqrt{x} .\sqrt{y} .\sqrt{z} = 200 \: \: \: \: \: - - - eq.(3)$

• Put the value of √x from eq.(1) in eq.(2) –

$\\ \bf \: \implies\: (20) .\sqrt{y} = 50 \sqrt{z}$

$\\ \bf \: \implies\: \sqrt{y} = \dfrac{50}{20} \sqrt{z}$

$\\ \bf \: \implies\: \sqrt{y} = \dfrac{5}{2} \sqrt{z}$

• Now multiply with √z –

$\\ \bf \: \implies\: \sqrt{y}. \sqrt{z} = \dfrac{5}{2} \sqrt{z}. \sqrt{z}$

$\\ \bf \: \implies\: \sqrt{y}. \sqrt{z} = \dfrac{5}{2}z\: \: \: \: \: - - - eq.(4)$

• Put the value of √x from eq.(1) in eq.(3) –

$\\ \bf \: \implies \: (20).\sqrt{y} .\sqrt{z} = 200$

$\\ \bf \: \implies \: \sqrt{y} .\sqrt{z} = \dfrac{200}{20}$

$\\ \bf \: \implies \: \sqrt{y} .\sqrt{z} = 10\: \: \: \: \: - - - eq.(5)$

• By eq.(4) & eq.(5) –

$\\ \bf \implies\dfrac{5}{2}z = 10$

$\\ \bf \implies5z =20$

$\\ \large\implies \red{\boxed{ \bf z =4}}$

• Now using eq.(5) –

$\\ \bf \: \implies \: \sqrt{y} .\sqrt{4} = 10$

$\\ \bf \: \implies \: \sqrt{y}(2)= 10$

$\\ \large\implies \red{\boxed{ \bf \sqrt{y} =5}}$

• Now let's find –

$\\\bf\implies \sqrt{x} + \sqrt{y} + \sqrt{z} = 20 + 5 + \sqrt{4}$

$\\\bf\implies \sqrt{x} + \sqrt{y} + \sqrt{z} = 20 + 5 +2$

$\\\bf\implies \sqrt{x} + \sqrt{y} + \sqrt{z} = 20 +7$

$\\\large\implies \blue{ \boxed{ \bf\sqrt{x} + \sqrt{y} + \sqrt{z} = 27}}$