Arrange the following in descending order. a=√(13)+√(11), b=√(15)+√(9), c=√(18)+√(6), d=√(7)+√(1

Arrange the following in descending order. a=√(13)+√(11),...

Key Concepts

Inequalities and Number Ordering

Arranging expressions in descending order relies on establishing inequalities between them. Understanding how to compare numerical sums through estimation and reasoning about relative magnitudes is crucial for ordering numbers, even when they include irrational components.

Square Root Estimation

This concept involves approximating the values of square roots, especially for non-perfect squares, by recognizing nearby perfect squares or using estimation techniques. Understanding this allows us to roughly calculate the value of each square root term, which is necessary for comparing sums of such terms.

Comparison of Sums Involving Irrational Numbers

When expressions consist of sums of square roots, each term must be approximated and then added to evaluate the sum. This process is essential to accurately compare the resulting values and determine their order, particularly when the expressions are not easily simplified.

Transcript

00:01 Hello students our question is arrange the following in descending order.

00:06 So we have given four different options we have to arrange them in descending order.

00:13 So let's write the question first.

00:16 So we have given a, a which is equal to root 13 plus root 11.

00:23 Route 13 plus root 13 plus root 11.

00:30 We have given b which is equal to b is equal to root 15 plus root 9 root 15 plus square root of 9 we have given c which is equal to root 18 plus root 6 root of 18 plus square root of 6 and we have given option b which is equal to root 7 plus root 17 root 7 plus root 17 so we have we have to arrange all this in descending order there it is a descending order is an order where we will first write the largest one then the smallest and the smallest will be written at the end so let's start our solution first we will find a square a square will be equal to root of 13 plus plus root of 11 whole square which which is equal to 13 plus 11 plus 2 into root 13 into root 11 which is equal to 13 plus 11 is equal to 24 plus 2 into this will be written a single root that is 13 multiply by 11 so it will become 13 multiply by 11 which is equal to 24 plus 2 root of 13 multiplied by 11 will be equal to 143 let's find b square b square will be equal to root of 15 plus root of 9 whole square that is square root of 15 plus square root of 9 whole square this will be open as a plus b whole square so a square will be equal to 15 plus b square will be equal to 9 plus 2 ab is equal to 2 x2 a b is equal to 2 into root 15 into root 9 so this is equal to 9 plus 15 equal to 24 plus 2 into this will be written a single root that is 15 multiply by 9 which is equal to 24 plus 2 root of 9 915 times is equal to 1305 now c square c square will be equal to root of 18 square root of 18 plus square root of 6 whole square will be equal to a plus b whole square is equal to a square that is square root of 18 square is to be equal to 18 square root of 9 square will be equal to 6 plus 2 into square root of 18 into square root of 6 which is equal to 18 plus 6 is also equal to 24 plus 2 into square root of 18 and square root of 6 will be written as a single root as 18 multiply by 6 which is equal to 24 plus 24 plus 2 into 108 100m now d square will be equal to d square will be equal to b square will be equal to square root of 7 plus square root of 17 whole square this will be equal to a plus bho square which is equal to a square that is square root of 7 will be square root of 17 that is this square will be equal to 17 plus 2 into square root of 7 into square root of 17 this is equal to 7 plus 17 will be 4 plus 2 into square root of 7 and 17 is written a single root 7 multiply by 17 which is equal 24 plus 2 into square root of square root of 17 7 times equal to 1 1 if we see here we see that so first part of the each question that is 24 plus 2 24 plus 2 24 plus 2 is the same so here square root of 43 1413 square root of 135 and square root of 135 and square root of 110 square root of 110...

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