Number System
- Let x be a rational number and y be an irrational number.
Is (x+y) necessarily an irrational number? Give an example in support of your answer. - Represent √4.7 geometrically on the number line.
- Find the value of a and b if
$$
\frac{7+3\sqrt{5}}{3+\sqrt{5}} – \frac{7-3\sqrt{5}}{3-\sqrt{5}} = a + b\sqrt{5}.
$$ - Rationalize the denominator of
$$
\frac{3}{3 + \sqrt{5} – 2}.
$$ - On simplification, the expression
$$
\frac{5^{n+2} – 6 \times 5^{n+1}}{13 \times 5^n – 2 \times 5^{n+1}}$$ equal to……. - If $$10^x = 64$$
find the value of
$$\frac{10^{x+1}}{10^x}$$ - The value of
$$\frac{3 – 2\sqrt{2}}{3 + 2\sqrt{2}}$$ is ______. - If $$\frac{9^y \times 3^2\times (3^\frac{-y}{2})^{-2}-(27)^x }{3^{3x}\times 2^3} = \frac{1}{27}$$ prove that y- x = 1.
- Prove that $$\frac{1}{1 + y^{a-b}} + \frac{1}{1 + y^{b-a}} = 1.$$
- Locate √3 and √5 on the number line.
Polynomial
Typing…………