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shamieh
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how does $$\frac{5700}{\sqrt{15,300}}$$ turn into $$\frac{570}{\sqrt{153}}$$ ??
MHB Question concerning simplification of numerical expression with square roots.
- Thread starter shamieh
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The expression $$\frac{5700}{\sqrt{15,300}}$$ simplifies to $$\frac{570}{\sqrt{153}}$$ by recognizing that 15,300 can be factored into 153 and 100. The square root of the product is then separated into the product of the square roots, leading to $$\frac{5700}{\sqrt{153} \cdot \sqrt{100}}$$. Simplifying further, the square root of 100 equals 10, allowing the expression to be rewritten as $$\frac{5700}{10\sqrt{153}}$$. Dividing 5700 by 10 results in 570, confirming the simplification.
Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...
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