Insert a rational number between and 2/9 and 3/8 arrange in descending order.
Insert two rational numbers between 1/3 and 1/4 and arrange in ascending order.
Insert two rational numbers between – 1/3 and – 1/2 and arrange in ascending order.
Insert three rational numbers between 1/3 and 4/5, and arrange in descending order.
Insert three rational numbers between 4 and 4.5.
Find six rational numbers between 3 and 4.
Find five rational numbers between 3/5 and 4/5.
Find ten rational numbers between -2/5 and 1/7.
Find six rational numbers between 1/2 and 2/3.
Prove that, √5 is an irrational number.
Prove that, √7 is an irrational number.
Prove that √6 is an irrational number.
Prove that 1/√11 is an irrational number.
Prove that √2 is an irrational number. Hence show that 3 — √2 is irrational.
Prove that √2 is an irrational number. Hence show that 3 — √2 is an irrational.
Prove that, √3 is an irrational number. Hence, show that 2/5×√3 is an irrational
number.
Prove that, √3 is an irrational number. Hence, show that 2/5×√3 is an irrational number.
Prove that √5 is an irrational number. Hence, show that -3 + 2√5 is an irrational number.
Prove that the following numbers are irrational:
(i) 5 +√2
(ii) 3 – 5√3
(iii) 2√3 – 7
(iv) √2 +√5
Locate √10 and √17 on the amber line.
Write the decimal expansion of each of the following numbers and say what kind
of decimal expansion each has:
(i) 36/100
(ii) 4 1/8
(iii) 2/9
(iv) 2/11
(v) 3/13
(vi) 329/400
Without actually performing the king division, State whether the following
rational numbers will have a terminating decimal expansion or a non-terminating
repeating decimal expansion:
(i) 13/3125
(ii) 17/8
(iii) 23/75
(iv) 6/15
(v) 1258/625
(vi) 77/210
Without actually performing the long division, find if 987/10500 will have terminating or non-terminating repeating decimal expansion.
Give reasons for your answer.
Write the denominator of the rational number 257/5000 in form 2^{m} \times 5^{r} where
m, n is non-negative integers. Hence, write its decimal expansion on without actual
division.
Write the decimal expansions of the following numbers which have terminating
decimal expansions:
(i) 17/8
(ii) 13/3125
(iii) 7/80
(v) 2^{2} \times 7 / 5^{4}
(vi) 237/1500
Write the decimal expansion of 1/7. Hence, write the decimal expression of?
2/7,3/7, 4/7, 5/7, and 6/7.
Express the following numbers in the form p/q’. Where p and q are both integers
and q≠0;
.. Classify the following numbers as rational or irrational:
(i) √23
(ii) √225
(iii) 0.3796
(iv) 7.478478
(v) 1.101001000100001…
(i) One irrational number between 1/3 and ½
(ii) One irrational number between -2/5 and ½
(iii) One irrational number between 0 and 0.1
Insert two irrational numbers between 2 and 3.
Write two irrational numbers between 4/9 and 7/11.
Find one rational number between √2 and √3.
Find two rational numbers between √12 and √15.
Insert irrational numbers between √5 and √7.
Insert two irrational numbers between √3 and √7.
Simplify the following:
(i) √45 – 3√20 + 4√5
(ii) 3√3 + 2√27 + 7/√3
(iii) 6√5 × 2√5
(iv) 8√15 ÷ 2√3
(v) √24/8 + √54/9
(vi) 3/√8 + 1/√2
(i) (5 + √7) (2 + √5)
(ii) (5 + √5) (5 – √5)
(v) (√2 + √3) (√5 + √7)
(vi) (4 + √5) (√3 – √7)
If √2 = 1.414, then find the value of
(i) √8 + √50 + √72 + √98
(ii) 3√32 – 2√50 + 4√128 – 20√18
If √3 = 1.732, then find the value of
(i) √27 + √75 + √108 – √243
(ii) 5√12 – 3√48 + 6√75 + 7√108
State which of the following are rational or irrational decimals.
(i) √(4/9), -3/70, √(7/25), √(16/5)
(ii) -√(2/49), 3/200, √(25/3), -√(49/16)
(i) -3√2
(ii) √(256/81)
(iii) √(27×16)
(iv) √(5/36)
State which of the following are irrational numbers.
(i) 3 – √(7/25)
(ii) -2/3 + ∛2
(iii) 3/√3
(iv) -2/7 ∛5
(v) (2 – √3) (2 + √3)
Prove the following are irrational numbers.
(i) ∛2
(ii) ∛3
(iii) ∜5
Find the greatest and the smallest real numbers.
(i) 2√3, 3/√2, -√7, √15
(ii) -3√2, 9/√5, -4, 4/3 √5, 3/2√3
Write in ascending order.
(i) 3√2, 2√3, √15, 4
(ii) 3√2, 2√8, 4, √50, 4√3
. Write in descending order.
(i) 9/√2, 3/2 √5, 4√3, 3√(6/5)
(ii) 5/√3, 7/3 √2, -√3, 3√5, 2√7
Arrange in ascending order.
Rationalize the following:
(i) 3/4√5
(ii) 5√7 / √3
(iii) 3/(4 – √7)
(iv) 17/(3√2 + 1)
(v) 16/ (√41 – 5)
(vi) 1/ (√7 – √6)
(vii) 1/ (√5 + √2)
(viii) (√2 + √3) / (√2 – √3)
. Simplify:
(i) (7 + 3√5) / (7 – 3√5)
(ii) (3 – 2√2) / (3 + 2√2)
(iii) (5 – 3√14) / (7 + 2√14)
Simplify:
[7√3 / (√10 + √3)] – [2√5 / (√6 + √5)] – [3√2 / (√15 + 3√2)]
[1/(√4 + √5)] + [1/(√5 + √6)] + [1/(√6 + √7)] + [1/(√7 + √8)] + [1/(√8 + √9)]
Given, find the value of a and b, if
(i) [3 – √5] / [3 + 2√5] = -19/11 + a√5
(ii) [√2 + √3] / [3√2 – 2√3] = a – b√6
(iii) {[7 + √5]/[7 – √5]} – {[7 – √5]/[7 + √5]} = a + 7/11 b√5
{[7 + 3√5] / [3 + √5]} – {[7 – 3√5] / [3 – √5]} = p + q√5
If √2 = 1.414, √3 = 1.732, find
(i) √2/(2 + √2)
(ii) 1/(√3 + √2)
If a = 2 + √3, find 1/a, (a – 1/a)
Solve:
If x = 5 – 2√6, find 1/x, \left(x^{2}-1 / x^{2}\right)
If p = (2-√5)/(2+√5) and q = (2+√5)/(2-√5), find the values of
(i) p + q
(ii) p – q
If x = (√2 – 1)/( √2 + 1) and y = (√2 + 1)/( √2 – 1), find
(i) x + y
(ii) xy
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