Hi, could someone please tell me how I would go about working these out: (the answer must be in the form a�ãb where a and b are integers and b is as small as possible.)
1) Simplify �ã500
2) Simplify �ã50 x �ã60
Also..
Simplify the following fractions so that there is no root in the denominator:
1/�ã5
12/�ã3
Thankyou so much!
by the way, where there is a box and the a, is meant to be a square root sign!
55-4=
solution: if a number is mutliplied by 7 and 56 is subracted from the product the result is equal to 14?find the number.
To simplify expressions involving square roots, you need to find the factors of the number inside the square root and determine if any of those factors have a square root that can be simplified further.
1) Simplify √500:
To simplify √500, start by finding the prime factors of 500, which are 2, 2, 5, and 5. There are two pairs of the same prime factors, 2 and 5. These pairs can be taken out of the square root and result in 2√5. Therefore, the simplified form of √500 is 2√5.
2) Simplify √50 x √60:
To simplify √50 x √60, you can combine the two square roots into one. Start by finding the prime factors of 50 and 60. The prime factors of 50 are 2, 5, and 5, while the prime factors of 60 are 2, 2, 3, and 5. From these factors, you can identify the common factors, which are 2 and 5. Taking these out of the square root, you get 2√(5 x 3) = 2√15.
Next, let's simplify the given fractions:
1) Simplify 1/√5:
To simplify this fraction, you want to remove the square root from the denominator. To do this, you can multiply both the numerator and denominator by the conjugate of the denominator, which is √5. The conjugate of √5 is -√5 (since the sign is changed). Multiply the numerator and denominator by -√5:
(1/√5) x (-√5) / (-√5) = -√5 / 5
Therefore, the simplified form of 1/√5 is -√5/5.
2) Simplify 12/√3:
To simplify this fraction, you can follow the same procedure as above. Multiply both numerator and denominator by the conjugate of √3, which is √3:
(12/√3) x (√3) / (√3) = 12√3 / 3
Simplifying further gives:
= 4√3
Therefore, the simplified form of 12/√3 is 4√3.
I hope this helps!