Irrational Numbers - ICSE STD 9 MATHEMATICS Questions

Q 1[1 Mark Question Answer]1 Mark

State if the following is a surd$. $Give reasons$.$$\sqrt[3]{-27}$

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Q 2[1 Mark Question Answer]1 Mark

State if the following is a surd. Give reasons.$\sqrt{2+\sqrt{3}}$

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Q 3[1 Mark Question Answer]1 Mark

State if the following is a surd. Give reasons.$\sqrt[3]{50} \cdot \sqrt[3]{20}$

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Q 4[1 Mark Question Answer]1 Mark

State if the following is a surd. Give reasons.$\sqrt[3]{4}$

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Q 5[1 Mark Question Answer]1 Mark

State if the following is a surd. Give reasons.$\sqrt{150}$

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Q 6[2 Mark Question Answer]2 Marks

Check whether the square of the following is rational or irrational$:\frac{3 \sqrt{2}}{2}$

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Q 7[2 Mark Question Answer]2 Marks

Check whether the square of the following is rational or irrational$:3 \sqrt{2}$

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Q 8[2 Mark Question Answer]2 Marks

State whether the following number is rational or irrational$:\left(\frac{\sqrt{5}}{3 \sqrt{2}}\right)^2$

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Q 9[2 Mark Question Answer]2 Marks

Insert a rational number between$:101$ and $102$

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Q 10[2 Mark Question Answer]2 Marks

Insert a rational number between$:8$ and $8.04$

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Q 11[3 marks sum]3 Marks

Simplify the following:$\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}$

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Q 12[3 marks sum]3 Marks

Simplify by rationalising the denominator in the following.$\frac{\sqrt{5}-\sqrt{7}}{\sqrt{3}}$

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Q 13[3 marks sum]3 Marks

Simplify by rationalising the denominator in the following.$\frac{3 \sqrt{2}}{\sqrt{5}}$

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Q 14[3 marks sum]3 Marks

Insert two irrational numbers between $3$ and $4.$

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Q 15[3 marks sum]3 Marks

Write the following in ascending order:$2 \sqrt{5}, \sqrt{3}$ and $5 \sqrt{2}$

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Q 16[4 marks sum]4 Marks

If $x=(4-\sqrt{15})$, find the values of $x+\frac{1}{x}$

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Q 17[4 marks sum]4 Marks

If $x=(4-\sqrt{15})$, find the values of $\frac{1}{x}$

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Q 18[4 marks sum]4 Marks

Simplify the following$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

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Q 19[4 marks sum]4 Marks

Simplify the following$\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}-\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}$

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Q 20[4 marks sum]4 Marks

Simplify the following$\frac{\sqrt{5}-2}{\sqrt{5}+2}-\frac{\sqrt{5}+2}{\sqrt{5}-2}$

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Q 21[5 marks sum]5 Marks

If $x=\frac{(2+\sqrt{5})}{(2-\sqrt{5})}$ and $y=\frac{(2-\sqrt{5})}{(2+\sqrt{5})}$, show that $\left(x^2-y^2\right)=144 \sqrt{5}$.

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Q 22[5 marks sum]5 Marks

If $x=(4-\sqrt{15})$, find the values of :$\left(x+\frac{1}{x}\right)^2$

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Q 23[5 marks sum]5 Marks

If $x=(4-\sqrt{15})$, find the values of $x^3+\frac{1}{x^3}$

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Q 24[5 marks sum]5 Marks

If $x = (4-\sqrt{15})$, find the values of $x^2+\frac{1}{x^2}$

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Q 25[5 marks sum]5 Marks

If $x = (7+4 \sqrt{3})$, find the values of :$\left(x+\frac{1}{x}\right)^2$

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Irrational Numbers question types

Irrational Numbers questions

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Irrational Numbers MATHEMATICS - Irrational Numbers

Irrational Numbers question types

Irrational Numbers questions

Generate a Irrational Numbers paper free