Question

examine whether this number is rational or irrational
with full solution
Best, complete and correct answer will get brainliested
promise☺️​

Answer 1

$\Large{\blue{\sf{ɢɪᴠᴇɴ:}}}$

• $\sf{[\sqrt{2}+\frac{1}{2}]^{2}}$

$\huge{\red{\sf{Solnʇıoυ:}}}$

$→\;{\sf{(\sqrt{2})^{2}+(\frac{1}{\sqrt{2}})^{2}+2×\sqrt{2}×\frac{1}{\sqrt{2}}}}$

$→\;{\sf{2+\frac{1}{2}+2}}$

$→\;{\sf{4+\frac{1}{2}}}$

$→\;{\sf{\frac{8+1}{2}}}$

$→\;{\sf{\frac{9}{2}}}$

$→\;{\bf{4.5}}$

→ ${\sf{\frac{45}{10} = \frac{p}{q}}}$ is a Rational Number.

$\Large{✓}$

Hope It Helps You ✌️

Answer 2

$\huge\bf{ՏOᒪᑌTIOᑎ}$

★ ${\sf{(\sqrt{2})^{2}+(\frac{1}{\sqrt{2}})^{2}+2×\sqrt{2}×\frac{1}{\sqrt{2}}}}$

★ ${\sf{2+\frac{1}{2}+2}}$

★ ${\sf{4+\frac{1}{2}}}$

★ ${\sf{\frac{8+1}{2}}}$

★ ${\sf{\frac{9}{2}}}$

★ ${\bf{4.5}}$

★ $\therefore$${\sf{In\:\frac{p}{q}\: form = \frac{45}{10}}}$