Question

simplify the following of rational and irrational number​

Answer 1

Step-by-step explanation:

=√16*7-√9*7+224/√4*7

=4√7-3√7+224/2√7

=√7+112/√7

=√7+112*√7/√7*√7

=√7+112*√7/7

=√7+16√7

=17√7

Answer 2

$\tt\purple{QUESTION:-}$

$\purple \diamond \small \tt{ \: \sqrt{112} - \sqrt{63} + \frac{224}{ \sqrt{28} } }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt\purple{SOLUTION:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small\tt{First \: do \: prime \: factorisation \: of \: 112,63 \: and \: 28}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\begin{array}{r||l} \small\tt{2}& \small\tt \purple{112}\\ \small\tt{2}& \small\tt \purple{56} \\ \small\tt{2} & \small \tt \purple{28}\\ \small\tt{2} & \small\tt \purple{14}\\ \small\tt{7} & \small\tt \purple{7} \\ & \small\tt \purple{1} \end{array}$

$\small \tt{112 =} \small \tt \purple{ \: 2 \times 2 \times 2 \times 2 \times 7}$

$\small \tt{112 =} \small \tt \purple{ \: 2\underbrace \times 2 \times 2 \underbrace \times 2 \times 7}$

$\small \tt{112 =} \small \tt \purple{ \: 2 \times 2 \times \sqrt{7}}$

$\small \tt{112 =} \small \tt \purple{ \: 4 \times \sqrt{7}}$

$\small \tt{112 =} \small \tt \purple{ \: 4 \sqrt{7}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\begin{array}{r||l} \small\tt{3}& \small\tt \purple{63}\\ \small\tt{3}& \small\tt \purple{21} \\ \small\tt{7} & \small \tt \purple{7}\\& \small\tt \purple{1}\end{array}$

$\small \tt{63 =} \small \tt \purple{ \: 3 \times 3 \times 7 }$

$\small \tt{63 =} \small \tt \purple{ \: 3\underbrace \times 3 \times 7}$

$\small \tt{63 =} \small \tt \purple{ \: 3 \times \sqrt{7} }$

$\small \tt{63 =} \small \tt \purple{ \: 3 \sqrt{7} }$

$\: \: \: \: \: \: \: \: \: \: \: \:$

$\begin{array}{r||l} \small\tt{2}& \small\tt \purple{28}\\ \small\tt{2}& \small\tt \purple{14} \\ \small\tt{7} & \small \tt \purple{7}\\& \small\tt \purple{1}\end{array}$

$\small \tt{28 =} \small \tt \purple{ \: 2 \times 2 \times 7 }$

$\small \tt{28 =} \small \tt \purple{ \: 2 \underbrace\times 2 \times 7 }$

$\small \tt{28 =} \small \tt \purple{ \: 2 \times \sqrt{7} }$

$\small \tt{28 =} \small \tt \purple{ \: 2 \sqrt{7} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple\diamond\small\tt{ \: Now \: back \: in \: the \: ques}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple \diamond \small \tt{ \: \sqrt{112} - \sqrt{63} + \frac{224}{ \sqrt{28} } }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small\tt\purple{Now \: Replace \: \sqrt{112} \: with \: } \small \tt{4 \sqrt{7} }$

$\small\tt\purple{ \: \sqrt{63} \: with } \small \tt{ \: 3 \sqrt{7} }$

$\small\tt\purple{ \: \sqrt{28} \: with } \small \tt{ \: 2 \sqrt{7} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple \diamond \small \tt{ \: 4\sqrt{7} - 3\sqrt{7} + \frac{224}{ 2(\sqrt{7}) } }$

$\purple \diamond \small \tt{ \: 4\sqrt{7} - 3\sqrt{7} + \frac{ \cancel224}{ \cancel2(\sqrt{7}) } }$

$\purple \diamond \small \tt{ \: \sqrt{7} + \frac{ 112}{ \sqrt{7} } }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small\tt\purple{\: Same \: the \: denominator}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple \diamond\tt{ \: \frac{ \sqrt{7} \times \sqrt{7} }{ \sqrt{7} } + \frac{ 112}{ \sqrt{7} } }$

$\purple \diamond\tt{ \: \frac{ { (\sqrt{7}) }^{2} }{ \sqrt{7} } + \frac{ 112}{ \sqrt{7} } }$

$\purple \diamond\tt{ \: \frac { 7 }{ \sqrt{7} } + \frac{ 112}{ \sqrt{7} } }$

$\purple \diamond\tt{ \: \frac{119}{ \sqrt{7} } }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small\tt\purple{Now, Rationalise \: the \: denominator}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple \diamond\tt{ \: \frac{119}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } }$

$\purple \diamond\tt{ \: \frac{119 \sqrt{7} }{ { (\sqrt{7}) }^{2} } }$

$\purple \diamond\tt{ \: \frac{ \cancel119 \sqrt{7} }{ { \cancel7 } } }$

$\diamond\small \tt \purple{ \: Ans\: is\: 17 \sqrt{7} }$