Subtract 4 5 from 7 5 . Is the answer rational or irrational?

Like surds are those surds which has same radicand We have to subtract 4 5 from 7 5 . Both surds are like surds because their radicand is same i.e 5 So, 7 5 - 4 5 = 7 - 4 5 = 3 5 An irrational number is a real number that cannot be expressed as a ratio of integers Thus, 3 5 is an irrational number.

Subtract 4 5 from 7 5 . Is the answer rational or irrational?

Like surds are those surds which has same radicand We have to subtract 4 5 from 7 5 . Both surds are like surds because their radicand is same i.e 5 So, 7 5 - 4 5 = 7 - 4 5 = 3 5 An irrational number is a real number that cannot be expressed as a ratio of integers Thus, 3 5 is an irrational number.

Simplify the following: 2 40 3 + 3 625 3 - 4 320 3

Given, 2 40 3 + 3 625 3 - 4 320 3 Convert radicand of all surds equal = 2 2 × 2 × 2 × 5 3 + 3 5 × 5 × 5 × 5 3 - 4 2 × 2 × 2 × 2 × 2 × 2 × 5 3 = 2 2 3 × 5 3 + 3 5 3 × 5 3 - 4 4 3 × 5 3 = 2 × 2 5 3 + 3 × 5 5 3 - 4 × 4 5 3 = 4 5 3 + 15 5 3 - 16 5 3 = 4 + 15 - 16 5 3 = 3 5 3 Thus, the required answer is 3 5 3

Multiply 40 3 and 16 3 .

Given, 40 3 × 16 3 Multiply the numbers outside of the square root sign together and then multiply the square roots together Simplify the surds = 2 × 2 × 2 × 5 3 × 2 × 2 × 2 × 2 3 = 2 × 5 3 × 2 × 2 3 = 4 × 2 3 × 5 3 = 4 × 2 × 5 3 = 4 10 3 Thus, the product is 4 10 3

Compute and give the answer in the simplest form: 2 72 × 5 32 × 3 50

Given, 2 72 × 5 32 × 3 50 Simplifying surds is where we rewrite a surd in its simplest form by ensuring the number underneath the root sign (this number is called the radicand) has no square numbers as factors. = 2 2 × 2 × 2 × 3 × 3 × 5 2 × 2 × 2 × 2 × 2 × 3 2 × 5 × 5 = 2 × 6 2 × 5 × 4 2 × 3 × 5 2 = 2 × 5 × 3 × 6 × 4 × 5 × 2 × 2 × 2 = 3600 × 2 2 = 7200 2 Thus, the simplest form is 7200 2

Given, 8 9 ÷ 6 6 Order of given surds is 9 and 6 As we know that a b = a 1 b 8 1 9 6 1 6 Now, 18 is the LCM of 6 and 9 8 2 18 6 3 18 = 8 2 18 6 3 18 As we know that a b c b = a c b = 8 2 6 3 1 18 = 8 × 8 6 × 6 × 6 1 18 = 8 27 1 18 = 2 3 3 1 18 = 2 3 1 6 = 2 3 6 Thus, the required answer is 2 3 6

Rationalise the denominator of 7 14

Rationalising the denominator is when we move a root (like a square root or cube root) from the bottom of a fraction to the top. We have to rationalise the denominator of 7 14 Multiply both numerator and denominator by the rationalising factor 14 . 7 14 = 7 14 × 14 14 = 7 14 14 = 14 2 Thus, the required answer is 14 2

Rationalise the denominator of 5 + 3 5 - 3

Rationalising the denominator is when we move a root (like a square root or cube root) from the bottom of a fraction to the top. We have to rationalise the denominator of 5 + 3 5 - 3 5 + 3 5 - 3 = 5 + 3 5 - 3 × 5 + 3 5 + 3 = 5 + 3 2 5 2 - 3 2 As we know that a + b 2 = a 2 + 2 a b + b 2 = 5 2 + 3 2 + 2 × 5 × 3 25 - 3 = 25 + 3 + 10 3 22 = 28 + 10 3 22 = 2 × 14 + 5 3 22 = 14 + 5 3 11 Thus, the required answer is 14 + 5 3 11