Square Roots of Decimals
Calculating square roots for numbers containing decimal points using appropriate grouping methods.
Definition
Finding the square root of a decimal number involves using the long division method with careful attention to the placement of the decimal point. Zeros can be appended to the decimal part to make pairs if necessary. The decimal point is placed in the quotient as soon as the decimal part of the number is reached during the division process.
Worked examples
To find sqrt(2.304), pair the whole part (2) and decimal part from left to right after the point (30 and add a 0 to make 40). The square root evaluates to 1.518 approximately.
To find sqrt(17.64), group as 17 and 64. The square root of 17.64 is 4.2 because 4.2 * 4.2 = 17.64.
To find sqrt(0.09), note that 0.09 has a decimal pair 09. The square root is 0.3 since 0.3 * 0.3 = 0.09.
Common mistakes
- • Placing the decimal point in the quotient at the wrong position by ignoring the pairs of decimal digits.
- • Pairing decimal digits incorrectly from left to right instead of right to left starting from the decimal point.
Introduction to Rational Numbers
Rational Numbers
Properties of Rational Numbers
Rational Numbers
Representation on Number Line
Rational Numbers
Rational Numbers Between Two Rational Numbers
Rational Numbers
Algebraic Expressions and Equations
Linear Equations in One Variable
Solving Equations with Variables on Both Sides
Linear Equations in One Variable