Sample Response: A rational number can be expressed as a whole number, a fraction, or decimal that has either terminating or repeating digits. A square root of a perfect square is rational. If it is none of these, then the number is irrational.
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D. The square root of 6
The value of the square root of six is √6 = 2.449489742783178...... and it doesn't terminate or terms do not repeat as well, after the decimal but only extends further, which is the property of the irrationalnumber. We can also prove that root 6 is irrational, 1 by using the method of contradiction or the other for using the method of long division.
Some of the important properties of the square root are as follows:
If the number is the perfect square number, then there exists a perfect square root. If the no ends with the even number of 0 (0’s), then it could have the square root. The 2 square root values could be multiplied. For example, √3 could be multiplied by √2, then the result can be √6.
The square root of six is a rational number if six it is the perfect square. It is an irrational number if this is not a perfect square. so 6 is not a perfect square, this is an irrationalnumber.
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Answer
Find out the how many shorter pieces can a seamstress cut.
To prove
Let us assume that the number of shorter pieces cut be x.
As given
A seamstress has a piece of cloth that is 3 yards long.
she cuts it into shorter lengths of 16 inches each.
As
1 yards = 36 inches
Now convert 3 yards into inches.
= 3 × 36
= 108 yards
Than the equation becomes
16x = 108
x = 6.75
Therefore the number of shorter pieces be 6 .
She can cut 6.75 shorter pieces
The division operation is one of the basic arithmetic operations
Common signs used are or
The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel
The division is actually an iterative subtraction operation (as many as the number of divisors)
Division is the opposite of multiplying
The general form of division can be stated by:
example:
7: 3 = 2 + 1
7 = dividend
3 = divisor
2 = quotient
1 = remainder
The form of division can also be expressed in terms of fractions
In the number above, the form of fraction obtained is the form of mixed fractions
Mixed fractions consist of integers and ordinary fractions
Division operation statement:
"7 divided by 3 equals 2 remainder 1
a piece of cloth that is 3 yards long
shorter lengths of 16 inches each
the number of shorter pieces that can be cut
Division operation statement:
"3 yards long divided by 16 inches*
We convert yards to inches
One yard is equal to 36 inches
1 yards = 36 inches
so for 3 yards :
x = 108 inches
Division operation :
108 inches : 16 inches
= 6.75 pieces
Divide 80 in a ratio of 3: 2
percent of 19.5 is 70.59
The average weight of the top 5 fish
Keywords: division, cloth, yards, inches
Simplifying
3X + 10 = 6X + 40
Reorder the terms:
10 + 3X = 6X + 40
Reorder the terms:
10 + 3X = 40 + 6X
Solving
10 + 3X = 40 + 6X
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-6X' to each side of the equation.
10 + 3X + -6X = 40 + 6X + -6X
Combine like terms: 3X + -6X = -3X
10 + -3X = 40 + 6X + -6X
Combine like terms: 6X + -6X = 0
10 + -3X = 40 + 0
10 + -3X = 40
Add '-10' to each side of the equation.
10 + -10 + -3X = 40 + -10
Combine like terms: 10 + -10 = 0
0 + -3X = 40 + -10
-3X = 40 + -10
Combine like terms: 40 + -10 = 30
-3X = 30
Divide each side by '-3'.
X = -10
Simplifying
X = -10