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Ratonalise the denominator in each of th...

Ratonalise the denominator in each of the following and hence evalute by taking `sqrt2=1.414, sqrt3=1.732 and sqrt(5)= 2.236` upto three places of decimal.
`(i)4/sqrt3`, (ii)`6/sqrt6`,`(iii)(sqrt10-sqrt5)/2`
`(iv)sqrt2/(2+sqrt2)` ,(v) `1/(sqrt3+sqrt2)`

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Let's rationalize the denominators for each of the given expressions step by step. ### (i) \( \frac{4}{\sqrt{3}} \) **Step 1:** Multiply the numerator and denominator by \( \sqrt{3} \): \[ \frac{4}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{3} \] ...
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NCERT EXEMPLAR ENGLISH-NUMBER SYSTEMS-SHORT ANSWER TYPE QUESTIONS
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  2. If x is a rational number and y is an irrational number, then both x\...

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  3. State whether the following statements is false ?

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  4. Check which of the following numbers is rational .

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  5. Find which of the variables x, y, z and u represent irrational numbers...

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  6. find three rational numbers between (i) –1 and –2 (ii) 0.1 and 0.11 (i...

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  7. Inset a rational number and an irrational number between the following...

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  8. Represent the following numbers on the number line 7,7.2,-3/2 and -12/...

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  9. Locate sqrt10 and sqrt17 on number line.

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  10. Represent geometically the following numbers on the number line

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  11. Express the following in the form P/q where p and q are integers and q...

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  12. Show that 0.142857142857…..=1/7.

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  13. Simplify the following (i) sqrt45-3sqrt20+4sqrt5 (ii) sqrt(24)/8 +...

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  14. Rationalise the denominator of the following (i) 2/(3sqrt3), (ii) sqr...

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  15. find the values of a and b in each of the following (i) (5+2sqrt3)/(7...

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  16. if a=2 + sqrt3, then find the value of (a-1/a).

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  17. Ratonalise the denominator in each of the following and hence evalute ...

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  18. simplify (i) (1^(3)+2^(3)+3^(3))^(1/2)(ii)(3/5)^(4)(8/5)^(-12)(32/5)...

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