Mathematics: 23 is between which two prefect squares? Between which two integers is √23

23 is between which two prefect squares? Between

HayleiMae

01.05.2022

Part 1) The length of each side of the square is about 4.47 units

Part 2) The length of its diagonal is about 6.32 units

Step-by-step explanation:

Part 1)

Find the length of each side of the square

In the right triangle TPQ

Applying the Pythagoras Theorem

$TQ^{2}=PQ^{2}-TP^{2}$

substitute the given values

$TQ^{2}=6^{2}-4^{2}$

$TQ^{2}=36-16$

$TQ^{2}=20$

$TQ=2\sqrt{5}\ units$ -----> exact value

$TQ=4.47\ units$ -----> approximate value

Part 2)

Find the length of the diagonal of the square

Applying the Pythagoras Theorem

$TR^{2}=TQ^{2}+QR^{2}$

we have

TQ=QR

$TQ=2\sqrt{5}\ units$

substitute

$TR^{2}=(2\sqrt{5})^{2}+(2\sqrt{5})^{2}$

$TR^{2}=40$

$TR=2\sqrt{10}\ units$ -----> exact value

$TR=6.32\ units$ ----> approximate value

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