To calculate: The simplification , by multiplication or division , of the expressions given below:a)\sqrt{15y} \cdot \sqrt{21y}

sanuluy

sanuluy

Answered question

2021-08-11

To calculate: The simplification , by multiplication or division , of the expressions given below:
a) 15y21y
b) 625c2d1035c5d3
image

Answer & Explanation

Fatema Sutton

Fatema Sutton

Skilled2021-08-12Added 88 answers

The answer is given below in the photo
Vasquez

Vasquez

Expert2021-12-28Added 669 answers

Step 1

Consider the expression,

15y×21y

As index in both the radicals is same, use the product property of radicals an×bn=abn , where a,b are any real numbers and n>1 is an integer.

15y×21y=15×21×y×y

=(3×5)×(3×7)×(y×y)

=32×35×y2

=(3×y)2×35

Use the product property of radicals, according to which, ann=a for any real number a and any integer n>1.

(3×y)2×35=(3×y)235

=3y35

Therefore, the multiplication of the given expression is 3y35

b) 6255×c2c5×d10d13=6255×c25×d1013

=125×c3×d93

=53×c3×(d3)33

Now, simplify the radicand and use the exponent property bn=1bn and ambm=(ab)m, where a,b are any real number and m,n are integers.

53×c3×(d3)33=(5d3)3c33

=(5d3c)33

=5d3c

Therefore, the division of the given expression is 5d3c

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