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### High School Mathematics6.13 Finding Square Root by Division Method

 Procedure: 1. Arrange the given expression in the descending power of x. 2. Find the square root of the first term in the expression. In the above example the first term is x4. Its square root is x2. This is the first term of the square root of the expression. 3. Write the square of x2, i.e. x4 below the first term of the expression and subtract the difference is zero. 4. The next two terms in the given expression is (-4x3 + 8x2) are to be brought down as the dividend for the next step. Double the first term of the square root and put it down as the first term of the next divisor i.e., 2x2 is to be written as the first term of the next divisor. The first term -4x3 of the dividend -43 + 8x2 is to be divided by the first term 2x2 of the next divisor. Then we get -2x. Now -2x is the second term of the square root of the given expression and second term of the new divisor. 5. Thus the new divisor becomes 2x2-2x. Multiply (2x2 - 2x) by -2x and the product -4x3 + 4x2 is to be brought down under the second dividend -4x3+8x2 and subtracted we get 4x2. 6. The remaining two terms in the given expression are to be brought down to make 4x2 - 8x + 4 as the new dividend. 7. Multiply x2 - 2x by 2 to get 2x2 - 4x as part of the new divisor. 8. Divide the first term 4x2 of 4x2 - 8x + 4 by 2x2 the first term of the part of new divisor. We get 2, this is the third term of the square root of the given expression and the third term of the new divisor. 9. Multiply the new divisor by 2 and subtract from the new dividend. 10. The remainder is zero. Hence the square root is x2 - 2x + 2. Directions: Solve the following problems using above method. Also write at least 10 examples of your own.
 Q 1: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.4x2 + 3x - 44x2 - 3x + 44x2 - 3x - 4 Q 2: Find the square root of x4 - 2x3 - 5x2 + 6x + 9.x2 - x - 3x2 - x + 3x2 + x - 3 Q 3: Find the square root of 16x4 + 16x3 + 12x2 + 4x + 1.4x2 - 2x - 14x2 + 2x - 14x2 + 2x + 1 Q 4: Find the square root of 44 - 4x3 + 12x2 - 16x + 16.x2 + 2x + 4x2 + 2x - 4x2 - 2x + 4 Q 5: Find the square root of 25x4 + 40x3 - 242 - 32x + 16.5x2 + 4x + 45x2 + 4x - 45x2 - 4x + 4 Q 6: Find the square root of x4 + 6x3 + 15x2 + 18x + 9.x2 - 3x + 3x2 + 3x + 3x + 3x2 + 3 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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