What should the number 3 + 5 be multiplied by to get a positive integer? Find the integer.

Given real number is 3 + 5 . The process of multiplying one rational number by another rational number to get rational number is called a rationalization. The rationalizing factor of 3 + 5 is 3 - 5 . ∴ 3 + 5 3 - 5 = 3 2 - 5 2 ∵ a + b a - b = a 2 - b 2 = 9 - 5 = 4 So, we have to multiply 3 + 5 by 3 - 5 to get an integer. Hence, 4 is the required integer.

What should the number 3 + 5 be multiplied by to get a positive integer? Find the integer.

Given real number is 3 + 5 . The process of multiplying one rational number by another rational number to get rational number is called a rationalization. The rationalizing factor of 3 + 5 is 3 - 5 . ∴ 3 + 5 3 - 5 = 3 2 - 5 2 ∵ a + b a - b = a 2 - b 2 = 9 - 5 = 4 So, we have to multiply 3 + 5 by 3 - 5 to get an integer. Hence, 4 is the required integer.

Find the value of 3 + 5 6 + 15 .

Given expression is 3 + 5 6 + 15 . ∴ 3 + 5 6 + 15 = 3 6 + 15 + 5 6 + 15 = 18 + 45 + 30 + 75 = 9 × 2 + 9 × 5 + 30 + 25 × 3 = 3 2 + 3 5 + 30 + 5 3 Hence, the value of 3 + 5 6 + 15 is 3 2 + 3 5 + 30 + 5 3 .

Find the value of 1 7 - 1 .

We need to find the value of 1 7 - 1 . Here, we need to simplify by rationalizing the denominator. Rationalizing factor of 7 - 1 is 7 + 1 . ∴ 1 7 - 1 = 1 7 - 1 × 7 + 1 7 + 1 = 7 + 1 7 2 - 1 2 ∵ a + b a - b = a 2 - b 2 = 7 + 1 7 - 1 = 7 + 1 6 Hence, the value of 1 7 - 1 is 7 + 1 6 .

What do you mean by real numbers? Locate 3 . 5 on the real number line geometrically.

Real numbers are the numbers which include both rational and irrational numbers. Locate 3 . 5 on number line 1 . Take any point A , then draw a line A B = 3 . 5 units 2 . Now, extend A B to point C such that B C = 1 units 3. Now, find out the mid point of A C say point O . Using O as a center draw a semi-circle with radius O C . 4. Draw a straight line from point B that is perpendicular to A C and intersecting semi-circle at point D .