Simplify :
18518+372−2162\dfrac{\sqrt{18}}{5\sqrt{18} + 3\sqrt{72} - 2\sqrt{162}}518+372−216218
19 Likes
Solving,
⇒18518+3×18×4−2×18×9⇒18518+3×2×18−2×3×18⇒1818(5+6−6)⇒15.\Rightarrow \dfrac{\sqrt{18}}{5\sqrt{18} + 3 \times \sqrt{18 \times 4} - 2 \times \sqrt{18 \times 9}} \\[1em] \Rightarrow \dfrac{\sqrt{18}}{5\sqrt{18} + 3 \times 2 \times \sqrt{18} - 2 \times 3 \times \sqrt{18}} \\[1em] \Rightarrow \dfrac{\sqrt{18}}{\sqrt{18}(5 + 6 - 6)} \\[1em] \Rightarrow \dfrac{1}{5}.⇒518+3×18×4−2×18×918⇒518+3×2×18−2×3×1818⇒18(5+6−6)18⇒51.
Hence, 18518+372−2162=15\dfrac{\sqrt{18}}{5\sqrt{18} + 3\sqrt{72} - 2\sqrt{162}} = \dfrac{1}{5}518+372−216218=51.
Answered By
11 Likes
Show that :
x2+1x2=34, if x =3+22x^2 + \dfrac{1}{x^2} = 34, \text{ if x } = 3 + 2\sqrt{2}x2+x21=34, if x =3+22.
32−2332+23+233−2\dfrac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \dfrac{2\sqrt{3}}{\sqrt{3} - \sqrt{2}}32+2332−23+3−223 = 11
Show that x is irrational, if :
(i) x2 = 6
(ii) x2 = 0.009
(iii) x2 = 27
Show that x is rational, if :
(i) x2 = 16
(ii) x2 = 0.0004
(iii) x2 = 1791\dfrac{7}{9}197
