Question

rds rationalization ex 3.1 first question second sub division​

Answer 1

Solution :

We know that -

$\bigstar\: \: \sf \: \dfrac{ \sqrt[n]{ a} }{ \sqrt[n]{b} } = \sqrt[n]{ \dfrac{a}{b} }$

$\longrightarrow\sf \: \dfrac{ \sqrt[4]{1250} }{ \sqrt[4]{2} }$

$\longrightarrow\sf \: \sqrt[4]{ \dfrac{1250}{2} }$

$\longrightarrow\sf \: \sqrt[4]{ 625}$

$\longrightarrow\sf \: \sqrt[4]{ ( {5})^{4} }$

$\longrightarrow\sf \: ( {5}^{4} ) { }^{ \frac{1}{4} }$

$\longrightarrow\sf \:5$

$\therefore \: \sf \: \dfrac{ \sqrt[4]{1250} }{ \sqrt[4]{2} } = 5$

Few useful identities relating to square roots :

• (√a)² = a

• √a√b = √ab

• √a/√b = √a/b

• (√a + √b)(√a - √b) = a - b

• (a + √b)(a - √b) = a² - b

• (√a ± √b)² = a ± 2√ab + b

• (√a + √b)(√c + √d) = √ac + √ad + √bc + √bd

Answer 2

$\bf \huge \fbox \red{answer : - }$

$\bf \huge \implies \frac{ \sqrt[4]{1250} }{ \sqrt[4]{ 2 } }$

$\bf \huge \implies \frac{1250 ^{\frac{1}{4}} }{ {1}^{ \frac{1}{4} } }$

$\bf \huge \implies( { \frac{1250}{2} )}^{ \frac{1}{4} }$

$\bf \huge \implies \: {625}^{ \frac{1}{4} }$

$\bf \huge \implies \: ({5})^{4( \frac{1}{4} )}$

$\bf \huge \implies \: {5}^{1}$

$\bf \huge\red{ \implies \: 5}$